To calculate the surface area of a cylinder with a radius of 7 yards and a height of 8 yards, we can use the formula:
\[
\text{Surface Area} = 2\pi r(h + r)
\]
Substituting the values:
- \( r = 7 \) yards
- \( h = 8 \) yards
- \( \pi \approx 3.14 \)
Now, we can plug in the numbers:
\[
\text{Surface Area} = 2 \times 3.14 \times 7 \times (8 + 7)
\]
\[
= 2 \times 3.14 \times 7 \times 15
\]
\[
= 2 \times 3.14 \times 105
\]
\[
= 6.28 \times 105
\]
\[
= 659.4 \text{ square yards}
\]
It appears that there was a misunderstanding since 659.4 square yards is not among the options you provided. Let's verify the calculations for \( 7 \) yards and \( 8 \) yards:
\[
\text{Surface Area} = 2 \times \pi \times r \times h + 2 \times \pi r^2
\]
Calculating the lateral area first:
\[
\text{Lateral Surface Area} = 2 \pi r h = 2 \times 3.14 \times 7 \times 8 = 2 \times 3.14 \times 56 = 352.64 \text{ square yards}
\]
Now calculating the area of the top and bottom:
\[
\text{Area of top and bottom} = 2 \pi r^2 = 2 \times 3.14 \times 7^2 = 2 \times 3.14 \times 49 = 307.76 \text{ square yards}
\]
Now adding both areas together:
\[
\text{Total Surface Area} = \text{Lateral Surface Area} + \text{Area of top and bottom} = 352.64 + 307.76 = 660.4 \text{ square yards}
\]
It seems there might be a mistake in getting the options. Based on accurate calculations, the surface area is approximately 660.4 square yards.
Please double-check the options you provided, or clarify if there is any additional context, since none of the answers match this calculation.
