Question

The surface area of this cylinder is 2,871.844 square yards. What is the height? Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth. r=17 h=?

Answer 1

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

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

Where:
- \( r \) is the radius
- \( h \) is the height

Given:
- Surface Area = 2,871.844 square yards
- \( r = 17 \) yards

First, let's plug in the values we know into the surface area formula.

1. Calculate \( 2\pi r^2 \):
\[
2\pi r^2 = 2 \times 3.14 \times (17)^2
\]
\[
(17)^2 = 289
\]
\[
2\pi r^2 = 2 \times 3.14 \times 289 \approx 1817.76 \text{ square yards}
\]

2. Now we can set up the equation for the surface area to solve for \( h \):
\[
2871.844 = 1817.76 + 2\pi rh
\]

3. Subtract \( 1817.76 \) from both sides:
\[
2871.844 - 1817.76 = 2\pi rh
\]
\[
1054.084 = 2\pi rh
\]

4. Substitute in \( r = 17 \):
\[
1054.084 = 2\pi (17)h
\]

5. Calculate \( 2\pi(17) \):
\[
2\pi(17) = 2 \times 3.14 \times 17 \approx 214.48
\]

6. Now, we have:
\[
1054.084 = 214.48h
\]

7. Solve for \( h \):
\[
h = \frac{1054.084}{214.48} \approx 4.91
\]

Rounding to the nearest hundredth, the height \( h \) is approximately:

\[
\boxed{4.91} \text{ yards}
\]