Find the surface area of a cylinder with a base diameter of 10 yd and a height of 8 yd

Write your answer in terms of JT, and be sure to include the correct unit.

To find the surface area of a cylinder, we use the formula:

\[
\text{Surface Area} = 2\pi r^2 + 2\pi rh
\]

Given:
- Diameter of the base \(d = 10\) yards
- Radius of the base \(r = \frac{d}{2} = \frac{10}{2} = 5\) yards
- Height \(h = 8\) yards

Now, plug in the values:

\[
\text{Surface Area} = 2\pi (5)^2 + 2\pi (5)(8)
\]

\[
\text{Surface Area} = 2\pi (25) + 2\pi (40)
\]

\[
\text{Surface Area} = 50\pi + 80\pi = 130\pi \text{ square yards}
\]

Since the problem asks to write the answer in terms of \(JT\), and assuming \(JT\) is a stand-in for \(\pi\), we substitute \(\pi\) with \(JT\):

\[
\text{Surface Area} = 130JT \text{ square yards}
\]

So, the surface area is \(130JT\) square yards.

Would you like any details or have any questions?

Here are some related questions:
1. How do you calculate the volume of the cylinder given the same dimensions?
2. What would be the surface area if the height was doubled?
3. How does changing the radius affect the surface area of a cylinder?
4. What is the lateral surface area of the cylinder?
5. How does the surface area of a cylinder compare to that of a cone with the same base and height?
6. Can you calculate the surface area of a hollow cylinder with the same dimensions?
7. How would the surface area change if the cylinder was open at the top?
8. What is the significance of \(\pi\) in the calculation of surface areas for circular shapes?

**Tip:** When solving geometry problems, always confirm that you’re using the correct units and have the right formulas for the specific shape you’re dealing with.

Learn how to calculate the surface area of a cylinder with a base diameter of 10 yards and a height of 8 yards. Understand the formula used, step-by-step calculation process, and the significance of \( JT \) (stand-in for \( \pi \)) in the context of geometry. Suitable for high school students studying geometry.

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