How to Find Radius of Cylinder Unveiling Geometric Truths

How to find radius of cylinder, a journey into the heart of geometric understanding, awaits us. Imagine a world of flowing lines and defined spaces, where the humble cylinder, a vessel of form and function, holds the key to unlocking profound truths. Within its circular embrace lies the radius, a silent guide, whispering secrets of volume, surface, and the very essence of its being.

As we delve into this exploration, we’ll uncover not just formulas, but a deeper connection to the principles that govern our world, learning to see the beauty and order hidden within seemingly simple shapes.

This exploration is more than just about numbers; it’s about seeing the world with a new perspective. The radius is not just a measurement; it is a key to unlock a deeper understanding of the world around us. From the smallest vial to the largest water tank, the radius dictates form, capacity, and the very way we interact with these objects.

We’ll journey through methods, examples, and real-world applications, transforming abstract concepts into tangible insights, ultimately gaining a new level of understanding and appreciation for the geometry of everyday life.

Understanding Cylinders and Their Properties

Alright, let’s talk cylinders! They’re everywhere, from your soda can to those giant water towers you see on road trips. Understanding them is key to a bunch of real-world problems, and it all starts with the basics.

Defining a Cylinder

A cylinder is a 3D geometric shape with two parallel circular bases connected by a curved surface. Think of it like a can of soup. These bases are identical circles, and the distance between them is the height of the cylinder.

Significance of the Radius

The radius is super important because it dictates everything about the cylinder’s size and shape. It’s the distance from the center of the circular base to any point on its edge. A bigger radius means a wider base, and that means a bigger cylinder overall. This impacts both the surface area and the volume.

Relationship Between Radius, Diameter, and Circumference

The circular base is defined by a few key measurements that are all linked. Understanding these relationships is fundamental to working with cylinders.

• Radius (r): As mentioned, this is the distance from the center of the circle to its edge.
• Diameter (d): The diameter is the distance across the circle, passing through the center. It’s always twice the radius. So,
  

  d = 2r

• Circumference (C): This is the distance around the circle, or its perimeter. It’s calculated using the formula:
  

  C = 2πr or C = πd

  , where π (pi) is a mathematical constant, approximately equal to 3.14159.

Methods for Finding the Radius

Alright, so you’ve got a cylinder, and you need to figure out its radius. We already covered the basics of cylinders, but sometimes you’re not given the radius directly. That’s where knowing the diameter comes in handy. It’s a super common piece of information you might have. Let’s break down how to get that radius when you’ve got the diameter.

Given the Diameter

Knowing the diameter is often the first step in figuring out the radius. The diameter is simply the distance across the circle, passing through the center. The radius, on the other hand, is the distance from the center of the circle to any point on its edge. There’s a super simple relationship between the two: the radius is always half the diameter.Here’s the deal:

Radius = Diameter / 2

It’s that easy! Let’s get into the step-by-step procedure:

1. Identify the Diameter: First, you need to know the diameter of the cylinder. This is usually given to you, or you might measure it.
2. Apply the Formula: Use the formula: Radius = Diameter / 2.
3. Calculate: Plug the diameter value into the formula and do the math.
4. State the Result: Make sure to include the units (e.g., cm, inches, meters) in your answer.

Let’s do an example. Say you have a cylinder with a diameter of 10 cm. Using the formula, the radius would be 10 cm / 2 = 5 cm.Now, let’s look at a table to illustrate this with some different diameter values and their corresponding radii:

Methods for Finding the Radius

Alright, so you’ve got your cylinder, and you need to figure out the radius, but maybe you’re not given it directly. No sweat! We’ve already covered some basics, and now we’re diving into more specific scenarios. Remember, the radius is just the distance from the center of the circular base to any point on its edge. Let’s get to it.

Methods for Finding the Radius: Given the Circumference

Sometimes, the only thing you know is the circumference of the circular base. No problem! The circumference is the distance around the circle, and we can totally use that to nail down the radius. It’s all about knowing the relationship between these two measurements.The key here is understanding the formula that links circumference and radius. The circumference (C) of a circle is calculated using the formula:

C = 2

• π
• r

Where:

• C represents the circumference.
• π (pi) is a mathematical constant, approximately equal to 3.14159.
• r represents the radius.

To find the radius when you know the circumference, you just need to rearrange the formula to solve for ‘r’. Here’s the procedure:

1. Start with the formula: C = 2
   • π
   • r
2. Isolate ‘r’: Divide both sides of the equation by 2

   π. This gives you

   r = C / (2 – π)

3. Plug in the circumference value: Substitute the known circumference value (C) into the formula.
4. Calculate: Perform the division to find the radius.

Let’s do a quick example. Say you have a cylinder with a circumference of 31.42 cm.

1. Formula

r = C / (2π)

• 2. Substitute

  r = 31.42 cm / (2

• 3.14159)

3. Calculate

r ≈ 31.42 cm / 6.28318 ≈ 5 cm

So, the radius of the cylinder is approximately 5 cm. Easy peasy!Here’s a table showing some different circumference values and their corresponding calculated radii. This should give you a good feel for how the numbers work.

Methods for Finding the Radius

Finding the radius of a cylinder is a common task in various fields, from engineering and architecture to everyday life. Knowing the radius is crucial for calculating other properties, such as the surface area and volume, and for understanding the cylinder’s overall dimensions. We’ve already covered some methods, and now we’ll focus on how to determine the radius when you know the cylinder’s volume and height.

Methods for Finding the Radius: Given the Volume and Height

When the volume and height of a cylinder are known, you can calculate the radius using a specific formula derived from the volume formula. This method is particularly useful when direct measurements of the cylinder’s circular base aren’t possible, but you have access to its volume (perhaps through calculations or given data) and its height. Let’s break down the process step-by-step.The key formula we’ll use is derived from the cylinder volume formula:

Volume (V) = π

• radius² (r²)
• height (h)

To find the radius, we rearrange this formula:

radius (r) = √(Volume (V) / (π

height (h)))

Here’s the step-by-step procedure:

• Identify the known values: First, you need to know the volume (V) of the cylinder and its height (h). Make sure the units of measurement are consistent (e.g., both in centimeters, meters, inches, etc.).
• Apply the formula: Substitute the known values of V and h into the formula: r = √(V / (π
  – h)).
• Calculate the intermediate value: Multiply π (approximately 3.14159) by the height (h).
• Divide the volume by the intermediate value: Divide the volume (V) by the result from the previous step.
• Calculate the square root: Take the square root of the result from the previous step. This will give you the radius (r).
• State the result with appropriate units: The final answer will be the radius, expressed in the same units as the height and any linear measurements used to determine the volume.

Let’s illustrate with an example. Suppose a cylinder has a volume of 1000 cubic centimeters (cm³) and a height of 10 cm.

• Identify the known values: V = 1000 cm³, h = 10 cm.
• Apply the formula: r = √(1000 / (π
  – 10)).
• Calculate the intermediate value: π
  – 10 ≈ 31.4159.
• Divide the volume by the intermediate value: 1000 / 31.4159 ≈ 31.831.
• Calculate the square root: √31.831 ≈ 5.64 cm.
• State the result with appropriate units: The radius of the cylinder is approximately 5.64 cm.

Methods for Finding the Radius

Alright, so we’ve covered the basics of cylinders and how to find their radius using a few different methods. Now, let’s dive into another scenario: what if you’re given the surface area and the height of the cylinder? This is a super common problem in geometry, and knowing how to solve it is key.

Methods for Finding the Radius: Given the Surface Area and Height

When you’re dealing with the surface area and height, you’ll need to work with a specific formula that incorporates both. The surface area of a cylinder includes the areas of the two circular bases and the lateral surface (the curved part). Let’s break down the formula and then work through some examples.The formula we’ll use is derived from the surface area (SA) formula of a cylinder:

SA = 2πr² + 2πrh

Where:

• SA = Surface Area
• r = radius
• h = height

To find the radius (r), we need to rearrange this formula. First, isolate the terms containing ‘r’:

• SA – 2πrh = 2πr²

Then, divide by 2π:

• (SA – 2πrh) / 2π = r²

Finally, take the square root of both sides to solve for r:

• r = √((SA – 2πrh) / 2π)

Okay, let’s look at some examples to see how this works in practice. Here’s a table with a few different surface area and height values, along with the calculated radius:

Practical Applications and Real-World Examples

Calculating the radius of a cylinder isn’t just a math problem; it’s a super useful skill in all sorts of real-world scenarios. From figuring out how much stuff a container can hold to designing buildings, understanding how to find the radius is essential. Let’s dive into some practical applications.

Calculating the Capacity of Cylindrical Tanks

Knowing the radius is critical for determining the volume, and therefore the capacity, of cylindrical tanks. This is super important in various industries, from agriculture to manufacturing.

• Water Storage: Imagine a cylindrical water tank used for irrigation on a farm. Let’s say the tank is 10 feet tall and has a volume of 785 cubic feet. To find the radius, we’d use the volume formula for a cylinder:
  

  Volume (V) = π
  – r²
  – h

  . Rearranging the formula to solve for the radius (r), we get:

  r = √ (V / (π
  – h))

  . Plugging in the numbers: r = √(785 / (π
  – 10)) which is approximately 5 feet. So, the radius of the tank is 5 feet. Knowing the radius allows the farmer to understand the tank’s capacity and manage water resources effectively.

• Chemical Storage: Chemical companies use cylindrical tanks to store various substances. Suppose a tank is designed to hold 10,000 gallons of a specific chemical. To ensure the tank meets the required volume, engineers must calculate the radius based on the desired height. If the tank is 20 feet tall, the calculation involves converting gallons to cubic feet (approximately 1,337 cubic feet per 10,000 gallons) and then applying the same volume formula and rearranging to find the radius.

  This accurate calculation ensures the tank safely contains the chemical.

• Fuel Storage: Oil and gas companies rely on large cylindrical tanks for fuel storage. The radius of these tanks is crucial for estimating the amount of fuel stored. For example, a tank might have a volume of 50,000 barrels (a barrel is about 5.615 cubic feet) and a height of 30 feet. The radius is then calculated using the same formula, ensuring accurate inventory management and efficient distribution of fuel resources.

Determining Dimensions of Cans and Containers

The radius is also a key measurement in the design and manufacturing of everyday items like cans and containers.

• Food Cans: Consider a standard can of soup. Manufacturers need to know the radius to determine the amount of material needed to produce the can and to calculate the can’s volume, which helps determine the net weight of the soup inside. For example, a can of soup might have a volume of 14.7 ounces and a height of 4 inches.

  Knowing the radius helps them calculate the surface area for labeling and the overall dimensions for packaging and shipping.

• Beverage Cans: Beverage companies use precise calculations to design cans for various drinks. The radius affects the can’s stability, the ease of handling, and the amount of liquid it can hold. If a can is designed to hold 12 ounces and has a specific height, the radius is calculated to ensure the can meets the volume requirements.
• Packaging: The radius is essential in designing cylindrical packaging for products like paper towels or rolls of tape. The radius dictates the diameter of the roll and influences how the product fits inside its packaging and how it will be displayed on store shelves. The radius also determines the total surface area for printing labels and branding.

Example: Calculating the Radius of a Water Tank

Let’s design a cylindrical water tank. We want the tank to hold 5,000 gallons of water. We know that 1 cubic foot is approximately 7.48 gallons. Therefore, the tank needs to hold approximately 5,000 / 7.48 = 668.45 cubic feet. Let’s decide on a height of 15 feet for the tank.Using the formula

r = √ (V / (π

h))

, we can calculate the radius

r = √(668.45 / (π15)) ≈ 3.74 feet. Therefore, the water tank would need a radius of approximately 3.74 feet to hold 5,000 gallons of water with a height of 15 feet. This calculation helps ensure the tank is built with the correct dimensions to meet its intended purpose.

Units of Measurement and Conversions

Alright, so you’ve got your cylinder, and you’re ready to find that radius. But hold up! Before you dive in, you gotta make sure you’re speaking the same language as your measurements. Using consistent units is absolutely crucial to avoid some serious math headaches and, you know, getting the wrong answer. Think of it like this: if you’re trying to build a bookshelf and your measurements are all over the place – inches, centimeters, feet – you’re gonna end up with a wonky, unusable mess.

Importance of Consistent Units

Using consistent units ensures that all measurements are compatible and can be accurately combined in calculations. This prevents errors and allows for reliable results when determining the radius or any other property of a cylinder. Inconsistent units lead to incorrect calculations and flawed conclusions.

Common Units of Measurement

Here’s the lowdown on some common units you’ll bump into when dealing with cylinders. Knowing these will keep you on the right track.

• Radius: Inches (in), centimeters (cm), feet (ft), meters (m)
• Diameter: Inches (in), centimeters (cm), feet (ft), meters (m)
• Circumference: Inches (in), centimeters (cm), feet (ft), meters (m)
• Volume: Cubic inches (in³), cubic centimeters (cm³), cubic feet (ft³), cubic meters (m³)
• Height: Inches (in), centimeters (cm), feet (ft), meters (m)

Conversion Factors for Length

Sometimes, you’ll get measurements in different units, and you’ll need to convert them. Don’t sweat it; it’s just a matter of multiplying by the right conversion factor. Here are a few you’ll find super handy:

• 1 inch (in) = 2.54 centimeters (cm)
• 1 foot (ft) = 12 inches (in)
• 1 foot (ft) = 30.48 centimeters (cm)
• 1 meter (m) = 100 centimeters (cm)
• 1 meter (m) = 3.281 feet (ft)

Illustrating the Conversion Process

Let’s look at how to convert between units with a cool table. This will help you visualize the process and nail those conversions.

Potential Challenges and Troubleshooting

Calculating the radius of a cylinder, while seemingly straightforward, can present some common pitfalls. These errors often stem from inaccurate measurements, misapplication of formulas, or simple calculation mistakes. Being aware of these potential challenges and knowing how to troubleshoot them is crucial for achieving accurate results.

Common Measurement Errors

Incorrect measurements are a primary source of errors when determining the radius of a cylinder. It’s essential to use precise measuring tools and to take measurements carefully.

• Incorrect Diameter Measurement: This is probably the most frequent mistake. Using a ruler instead of calipers, or not measuring the widest point, can lead to inaccurate diameter readings. This error directly impacts the radius calculation, as the radius is half the diameter.
• Incorrect Height Measurement: When calculating the radius using volume or surface area, the height of the cylinder is often needed. Measuring the height incorrectly, especially if the cylinder isn’t perfectly upright, will skew the final result.
• Using the Wrong Units: Mixing units (e.g., using inches for the diameter and centimeters for the height) will produce an incorrect answer. Always ensure consistency in units before performing calculations.

Formula Application Issues

Misunderstanding or misapplying the formulas for volume, surface area, or other relevant properties can lead to incorrect radius calculations.

• Using the Wrong Formula: Choosing the wrong formula for the given information is a common mistake. For example, using the surface area formula when you have the volume. Make sure to use the correct formula based on the information provided.
• Incorrect Substitution: Even with the right formula, substituting the wrong values into the equation is easy. Double-check that you’re plugging the correct measurements (diameter, height, volume, surface area) into the appropriate places in the formula.
• Order of Operations Errors: Remember to follow the order of operations (PEMDAS/BODMAS) when solving the equation. Failing to do so can result in an incorrect answer.

Troubleshooting Tips for Measurement Errors

If you suspect a measurement error, follow these troubleshooting steps.

• Re-measure: Take the measurement again, paying extra attention to the details. Use the correct tools (calipers for diameter, a level surface for height).
• Check the Tool: Ensure your measuring tools are functioning correctly and are calibrated if necessary.
• Measure Multiple Times: If possible, take several measurements and calculate the average. This can help minimize the impact of any single measurement error.

Troubleshooting Tips for Formula Application Issues

If you suspect a formula application issue, use these troubleshooting steps.

• Review the Formula: Double-check the formula you’re using. Make sure it’s the correct one for the information provided.
• Verify Substitutions: Carefully review your substitutions. Ensure you’ve plugged in the correct values for each variable in the formula.
• Check the Order of Operations: Go through your calculations step-by-step, making sure you’ve followed the order of operations correctly.

Examples of Incorrect Calculations and Corrections

Let’s look at some examples of incorrect calculations and how to fix them.

Example 1: Incorrect Diameter Measurement

Problem: You measure the diameter of a cylinder with a ruler and get 5 inches, but the actual diameter is 6 inches.

Incorrect Calculation: Radius = 5 inches / 2 = 2.5 inches

Correct Calculation: Radius = 6 inches / 2 = 3 inches

The error in the diameter measurement directly impacts the radius calculation. A small error in the diameter can lead to a significant difference in the calculated radius, especially when dealing with larger cylinders.

Example 2: Using the Wrong Formula

Problem: You are given the surface area of a cylinder and its height and try to calculate the radius using the volume formula.

Incorrect Formula: Volume = π
– radius ²
– height

Correct Formula (to use surface area): Surface Area = 2π
– radius
– height + 2π
– radius ²

Using the incorrect formula will lead to an incorrect result. The choice of the correct formula is crucial to calculate the radius.

Example 3: Order of Operations Error

Problem: When solving for radius after having the volume, the following calculation is made without using the order of operations correctly.

Given: Volume = 100 cm ³, Height = 10 cm. The incorrect calculation is: radius ² = 100 / π
– 10

Incorrect Calculation: radius ² = 100 / 3.14
– 10 = 318.47. Radius = sqrt(318.47) = 17.85 cm

Correct Calculation: radius ² = 100 / (π
– 10) = 100 / 31.4 = 3.18. Radius = sqrt(3.18) = 1.78 cm

Failure to follow the order of operations can lead to significantly incorrect answers.

Visual Representations and Illustrations

Understanding the geometry of a cylinder is significantly aided by visual representations. Diagrams and illustrations clarify the relationships between the cylinder’s components, especially the radius. Visual aids transform abstract concepts into tangible forms, making it easier to grasp the principles of calculation and application.

Diagram of Cylinder Components

A detailed diagram provides a clear breakdown of a cylinder’s essential parts. The visual representation highlights each element and their relationship to one another.A cylinder is depicted as a three-dimensional shape, a can-like structure. The diagram is a side view, and it shows:

• The
  -height* of the cylinder, a vertical line segment extending from the center of one circular base to the center of the other. This line is labeled “h”.
• The
  -radius*, a line segment extending from the center of one of the circular bases to a point on the circumference of that base. This is labeled “r”.
• The
  -diameter*, a line segment that passes through the center of a circular base and connects two points on the circumference. This is labeled “d” and is shown as twice the radius. The relationship is represented as:

  d = 2r

• The
  -circumference* of the circular base, represented by a curved line encircling the base. It is labeled “C”. The circumference is linked to the radius through the formula:

  C = 2πr

Steps for Drawing a Cylinder and Labeling Key Parts

Creating a basic cylinder diagram is a useful skill. These steps guide the drawing process.

1. Start by drawing two congruent circles, representing the top and bottom bases of the cylinder. Ensure the circles are aligned vertically.
2. Connect the corresponding points on the circumferences of the circles with two parallel lines. These lines represent the lateral surface of the cylinder.
3. Draw a vertical line segment connecting the centers of the two circles. This represents the height (h) of the cylinder.
4. Draw a line segment from the center of one of the circles to a point on its circumference. This represents the radius (r).
5. Label the height, radius, and any other relevant measurements. Label the circumference as well.

3D Illustration of a Cylinder with Highlighted Radius

A 3D illustration provides a more immersive understanding of a cylinder’s structure. It enhances the ability to visualize the radius in context.The illustration showcases a cylinder in three dimensions, allowing for a realistic perspective.

• The cylinder appears as a solid object, with its circular bases and curved lateral surface.
• The radius is highlighted using a different color, such as red, to distinguish it clearly from other parts of the cylinder.
• The radius line extends from the center of one of the circular bases to a point on the circumference, demonstrating its function as a measure of distance from the center.
• The diagram might include arrows or labels pointing to the radius, height, and other key features.

Advanced Considerations: Irregular Cylinders: How To Find Radius Of Cylinder

Alright, so we’ve covered finding the radius of perfect, symmetrical cylinders. But what happens when things aren’t so neat? Real-world objects often aren’t perfect cylinders. They might be slightly warped, have dents, or be composed of different materials, making finding the radius a bit more complicated. Let’s dive into how to handle those messy situations.

Challenges in Finding the Radius of an Irregular Cylinder

Dealing with irregular cylinders presents some unique hurdles. The simple formulas we’ve used before might not cut it, and we need to think outside the box.

Limitations of Standard Formulas for Non-Ideal Cylinders, How to find radius of cylinder

Standard formulas assume a perfect, uniform shape. This assumption falls apart when dealing with irregularities.* Non-Uniformity: If the cylinder isn’t perfectly round, using the standard formula will lead to inaccurate results. The diameter, and consequently the radius, will vary depending on where you measure it.

Surface Irregularities

Dents, bulges, or variations in the surface material can significantly impact measurements. For example, a dent in a metal pipe will change its internal volume, affecting the radius calculation if volume is used.

Non-Constant Cross-Section

Standard formulas assume a consistent circular cross-section throughout the cylinder’s length. If the cylinder tapers or changes shape, the radius isn’t constant, and a single calculation won’t be accurate.

Alright, so you need to find the radius of a cylinder, right? Remember, it’s half the diameter. But hey, sometimes things go wrong, and you need a fix. If you’re dealing with hydraulic cylinders and need a rebuild, you might be wondering, well, who rebuilds hydraulic cylinders near me ? Once you get those cylinders sorted, calculating the radius is a breeze again, just remember that simple formula!

Methods or Estimations for Irregular Shapes

Because standard formulas are limited, alternative approaches are necessary. These methods rely on approximation and understanding the limitations.

Alternative Approaches for Irregular Shapes

When dealing with non-ideal cylinders, a more flexible approach is needed. Here’s a breakdown of some alternative methods.* Multiple Measurements and Averaging: Measure the diameter at several points along the cylinder’s length and take the average. This helps to account for minor variations in shape. This is particularly useful for cylinders with slight warping. For instance, if you’re measuring a slightly bent PVC pipe, taking diameter measurements every few inches and averaging the results will give you a better radius estimate than a single measurement.* Volume Displacement: If you can submerge the cylinder in a liquid and measure the volume of liquid displaced, you can use the volume formula, solving for the radius, and accounting for the length.

This works well if you can’t directly measure the diameter due to access or shape constraints. This method works well for irregularly shaped objects where a direct measurement is difficult.

Volume = π

• radius²
• height

* Sectioning and Integration (Calculus-Based): For more complex shapes, you might need to use calculus. Imagine dividing the cylinder into infinitesimally small slices and integrating the area of each slice. This is a more advanced technique but can be very accurate. This is used in engineering to calculate the volume of complex shapes.* Laser Scanning or 3D Modeling: Modern technology can provide highly accurate measurements.

Laser scanners can create a 3D model of the cylinder, allowing for precise radius measurements at any point. 3D modeling software can also be used to estimate the radius from photographs or other data. This method is used extensively in manufacturing and quality control to ensure parts meet specifications. For example, imagine a 3D model of a damaged fuel tank on an aircraft.

The model could be used to precisely determine the extent of damage and calculate remaining volume.* Comparison with Known Shapes: If the irregular cylinder resembles a known shape, like a frustum (a cone with the top cut off), you can adapt formulas accordingly. This requires careful observation and an understanding of geometric principles. For example, if a bottle has a slightly tapered shape, you could estimate the radius at different points along its height by comparing it to a frustum.

Wrap-Up

As we conclude our exploration of how to find radius of cylinder, let us carry the wisdom gained within our hearts. Remember that the journey of learning is a continuous cycle of discovery, just like the circle itself, always returning to the starting point, yet changed by the experience. May this knowledge empower you to see the world with a renewed sense of wonder, to find the hidden beauty in the simplicity of form, and to embrace the joy of understanding the fundamental principles that shape our universe.

Go forth and apply this understanding, not just to solve problems, but to see the world with a deeper, more meaningful perspective.

Questions Often Asked

Why is the radius so important in understanding a cylinder?

The radius is the fundamental building block. It directly influences the cylinder’s volume, surface area, and even its stability. Knowing the radius allows you to calculate the cylinder’s capacity and how much material is needed to create it.

What if I only have the cylinder’s volume and height, but not the diameter or circumference?

You can still find the radius! Using the volume and height, you can rearrange the volume formula (Volume = π
– radius²
– height) to solve for the radius: radius = √ (Volume / (π
– height)).

Can I use these formulas for cylinders that are not perfectly straight?

These formulas are designed for ideal cylinders. If a cylinder is irregular, the calculations will be estimations. You might need to break the shape into smaller, more regular sections or use advanced techniques.

How do I handle different units of measurement?

Consistency is key! Make sure all your measurements are in the same units (e.g., all in inches or all in centimeters) before performing calculations. If necessary, convert units using the appropriate conversion factors.

What are some common mistakes when calculating the radius?

A common mistake is using the diameter instead of the radius in the formulas. Always remember that the radius is half the diameter. Also, be careful with units and ensure you are using the correct formulas for the given information.