Question

The surface area of this cylinder is 2,903.872 square meters. What is the height?
The radius is 17
Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.

Answer 1

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

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

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

Given that the surface area \( S \) is 2903.872 square meters and the radius \( r \) is 17 meters, we can substitute these values into the formula:

\[
2903.872 = 2\pi(17)^2 + 2\pi(17)h
\]

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

\[
2\pi(17^2) = 2\pi(289) = 578\pi
\]

Using \( \pi \approx 3.14 \):

\[
578\pi \approx 578 \times 3.14 \approx 1810.32
\]

Now substituting back into the surface area equation:

\[
2903.872 = 1810.32 + 34\pi h
\]

Where \( 2\pi(17) = 34\pi \). Now, we can use \( \pi \approx 3.14 \) to calculate \( 34\pi \):

\[
34\pi \approx 34 \times 3.14 \approx 106.76
\]

Now our equation becomes:

\[
2903.872 = 1810.32 + 106.76h
\]

Isolating \( h \):

\[
2903.872 - 1810.32 = 106.76h
\]

\[
1093.552 = 106.76h
\]

Now, divide both sides by 106.76 to solve for \( h \):

\[
h = \frac{1093.552}{106.76} \approx 10.26
\]

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

\[
\boxed{10.26} \text{ meters}
\]