Question

The surface area of this cylinder is 3,106.716 square feet. What is the height?

































Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.

r = 17

Answer 1

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

\[
A = 2\pi r^2 + 2\pi rh
\]

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

Given:
- \(A = 3106.716\) square feet
- \(r = 17\)

First, we can substitute the given values into the surface area formula:

\[
3106.716 = 2\pi (17^2) + 2\pi (17)h
\]

Calculating \(2\pi(17^2)\):

\[
17^2 = 289 \quad \text{so} \quad 2\pi(289) \approx 2 \times 3.14 \times 289 \approx 1811.56
\]

Now we substitute this back into the surface area equation:

\[
3106.716 = 1811.56 + 2\pi(17)h
\]

Next, isolate \(2\pi(17)h\):

\[
3106.716 - 1811.56 = 2\pi(17)h
\]
\[
1295.156 = 2\pi(17)h
\]

Calculating \(2\pi(17)\):

\[
2\pi(17) \approx 2 \times 3.14 \times 17 \approx 214.48
\]

Now we substitute this value back into the equation for height \(h\):

\[
1295.156 = 214.48h
\]

Now, solve for \(h\):

\[
h = \frac{1295.156}{214.48} \approx 6.04
\]

Thus, rounding to the nearest hundredth, the height of the cylinder is approximately:

\[
\boxed{6.04} \text{ feet.}
\]