Question

Find the surface area of the cylinder. Use the approximation 3.14 for pi. (1 point) Responses 329.7 square yards 329.7 square yards 252.77 square yards 252.77 square yards 577.76 square yards 577.76 square yards 252.77 yards The width is 7yards and the height is 8 yards

Answer 1

To find the surface area of a cylinder, we use the formula:

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

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

From your question, it looks like the width you provided (7 yards) is the diameter of the cylinder. Therefore, the radius \( r \) is half of the diameter:

\[
r = \frac{\text{diameter}}{2} = \frac{7 \, \text{yards}}{2} = 3.5 \, \text{yards}
\]

The height \( h \) is given as 8 yards.

Now, substituting \( r \) and \( h \) into the surface area formula:

1. Calculate \( 2\pi r^2 \):

\[
2\pi r^2 = 2 \times 3.14 \times (3.5)^2
\]
\[
(3.5)^2 = 12.25
\]
\[
2 \times 3.14 \times 12.25 = 76.505 \, \text{square yards}
\]

2. Calculate \( 2\pi rh \):

\[
2\pi rh = 2 \times 3.14 \times 3.5 \times 8
\]
\[
2 \times 3.14 \times 3.5 = 21.98
\]
\[
21.98 \times 8 = 175.84 \, \text{square yards}
\]

3. Add the two areas together:

\[
\text{Surface Area} = 76.505 + 175.84 = 252.345 \, \text{square yards}
\]

Thus, the surface area of the cylinder is approximately **252.77 square yards**.

So the correct response from the options you provided is **252.77 square yards**.