Question

The surface area of this cylinder is 3,737.3536 square feet. What is the height? Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth. 17.2 ft h h ≈ feet

Answer 1

To find the height of the cylinder given its surface area, we use the formula for the surface area \( A \) of a cylinder, which is:

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

where:
- \( A \) is the surface area,
- \( r \) is the radius, and
- \( h \) is the height.

Given the surface area \( A = 3737.3536 \) square feet, we need to rearrange the equation to solve for the height \( h \).

1. We need the value of \( r \) (the radius of the cylinder) in order to solve for \( h \). Since you did not provide the radius, I will proceed with a general equation of \( h \).

2. Rearranging the surface area formula:

\[
3737.3536 = 2 \cdot 3.14 \cdot r(h + r)
\]

3. Simplifying this gives:

\[
3737.3536 = 6.28r(h + r)
\]

4. Now, express \( h \):

\[
h + r = \frac{3737.3536}{6.28r}
\]

\[
h = \frac{3737.3536}{6.28r} - r
\]

At this point, we need the specific value for \( r \) (which is not provided).

If you assume the radius \( r \) as 17.2 ft which seems to be indicated in the question, we can substitute that into the equation:

\[
h = \frac{3737.3536}{6.28 \cdot 17.2} - 17.2
\]

Calculating this:

1. Calculate \( 6.28 \cdot 17.2 \):

\[
6.28 \times 17.2 \approx 107.136
\]

2. Now substitute into the equation for \( h \):

\[
h = \frac{3737.3536}{107.136} - 17.2
\]

3. Calculate \( \frac{3737.3536}{107.136} \):

\[
\frac{3737.3536}{107.136} \approx 34.87
\]

4. Then calculate \( h \):

\[
h \approx 34.87 - 17.2 \approx 17.67
\]

So the height \( h \) rounded to the nearest hundredth is:

\[
\boxed{17.67} \text{ feet}
\]