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.

Answer 1

To calculate the height of the cylinder given its surface area, we can use the formula for the surface area \( S \) of a cylinder, which is given by:

\[
S = 2\pi r(h + r)
\]

Where:
- \( S \) is the surface area,
- \( r \) is the radius,
- \( h \) is the height.

Given that the surface area \( S \) is 3,106.716 square feet, we can rearrange the formula to solve for height \( h \):

\[
3,106.716 = 2\pi r(h + r)
\]

However, to find the height \( h \), we need either the radius \( r \) or more information relating to it.

Assuming we do not have a specific radius, we need to derive an expression for \( h \) in terms of \( r \):

1. Rearranging the equation for \( h \):

\[
h = \frac{3,106.716}{2\pi r} - r
\]

Substituting \( \pi \approx 3.14 \):

\[
h = \frac{3,106.716}{2 \times 3.14 r} - r
\]

\[
h = \frac{3,106.716}{6.28 r} - r
\]

If you know the radius \( r \), you can substitute it into the equation above to find the height \( h \).

Please provide the radius \( r \) of the cylinder so that we can calculate the height accurately. If no radius is given and you need a specific height using a particular radius, please specify that radius.