Question

Radius is 17
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 find the height of the cylinder given the radius and the surface area, we can use the formula for the surface area \( S \) of a cylinder:

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

where:
- \( S \) is the surface area,
- \( r \) is the radius,
- \( h \) is the height,
- \( \pi \) is approximately 3.14.

We know:
- \( S = 3106.716 \) square feet,
- \( r = 17 \) feet.

Substituting these values into the surface area formula, we get:

\[
3106.716 = 2 \cdot 3.14 \cdot 17 \cdot (h + 17)
\]

Calculating \( 2 \cdot 3.14 \cdot 17 \):

\[
2 \cdot 3.14 = 6.28,
\]
\[
6.28 \cdot 17 = 106.76.
\]

Now substituting \( 106.76 \) back into the equation:

\[
3106.716 = 106.76(h + 17).
\]

Next, we can divide both sides by \( 106.76 \):

\[
h + 17 = \frac{3106.716}{106.76}.
\]

Calculating the right side:

\[
\frac{3106.716}{106.76} \approx 29.1.
\]

Now we have:

\[
h + 17 \approx 29.1.
\]

Subtracting 17 from both sides gives us:

\[
h \approx 29.1 - 17.
\]
\[
h \approx 12.1.
\]

Therefore, the height \( h \) of the cylinder, rounded to the nearest hundredth, is:

\[
\boxed{12.10} \text{ feet.}
\]