Question

The surface area of a cylinder is 1,657.92 square yards. It has a diameter of 16 yards. Find the height. Use 3.14 for π
.(1 point)
_ yards

Answer 1

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

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

Where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder.

Given:
- The diameter of the cylinder is 16 yards, so the radius \( r \) is half of that:

\[
r = \frac{16}{2} = 8 \text{ yards}
\]

- The surface area is given as 1,657.92 square yards.
- We will use \( \pi \approx 3.14 \).

Substituting the values into the surface area formula:

\[
1,657.92 = 2 \times 3.14 \times (8^2) + 2 \times 3.14 \times 8 \times h
\]

First, calculate \( 8^2 \):

\[
8^2 = 64
\]

Now substitute that back into the equation:

\[
1,657.92 = 2 \times 3.14 \times 64 + 2 \times 3.14 \times 8 \times h
\]

Calculating \( 2 \times 3.14 \times 64 \):

\[
2 \times 3.14 \times 64 = 6.28 \times 64 = 401.92
\]

Now our equation looks like this:

\[
1,657.92 = 401.92 + 2 \times 3.14 \times 8 \times h
\]

Next, we need to isolate the term with \( h \):

\[
1,657.92 - 401.92 = 2 \times 3.14 \times 8 \times h
\]

Calculating the left side:

\[
1,657.92 - 401.92 = 1,256
\]

Now, calculating \( 2 \times 3.14 \times 8 \):

\[
2 \times 3.14 \times 8 = 6.28 \times 8 = 50.24
\]

So now our equation is:

\[
1,256 = 50.24 \times h
\]

Now, solve for \( h \):

\[
h = \frac{1,256}{50.24}
\]

Calculating the height:

\[
h \approx 25
\]

Thus, the height of the cylinder is approximately:

\[
\boxed{25} \text{ yards}
\]