To find the surface area \( A \) of a cylinder, you can use the formula:
\[ A = 2\pi r(h + r) \]
where:
- \( r \) is the radius,
- \( h \) is the height,
- \( \pi \) is approximately 3.14.
Given:
- Height \( h = 8 \) yards
- Radius \( r = 7 \) yards
Now, substituting the values into the formula:
- Calculate \( h + r \):
\[ h + r = 8 + 7 = 15 \]
- Substitute \( r \) and \( h + r \) into the surface area formula:
\[ A = 2 \times 3.14 \times 7 \times 15 \]
- Calculate \( 2 \times 3.14 \):
\[ 2 \times 3.14 = 6.28 \]
- Now, calculate \( 6.28 \times 7 \):
\[ 6.28 \times 7 = 43.96 \]
- Finally, multiply that by 15:
\[ A = 43.96 \times 15 = 659.4 \]
So the total surface area of the cylinder is:
\[ A \approx 659.4 \text{ square yards} \]
However, since this result does not match any of the listed options, let's check for any discrepancies:
Recalculation of individual sections:
- Compute the lateral area \( 2\pi rh \):
\[ Lateral Area = 2 \times 3.14 \times 7 \times 8 = 2 \times 3.14 \times 56 = 352.32 \]
- Compute the area of the two circles (top and bottom):
\[ Area_{base} = \pi r^2 = 3.14 \times (7^2) = 3.14 \times 49 = 153.86 \]
Based on the area of the two bases:
\[ Area_{two\ bases} = 2 \times Area_{base} = 2 \times 153.86 = 307.72 \]
Now, add the lateral and base areas together to find total surface area:
\[ Total\ Surface\ Area = Lateral\ Area + Area_{two\ bases} = 352.32 + 307.72 = 660.04 \]
There may have been a rounding difference, but since the surface area calculated still doesn't match any of the options provided:
It appears that \( 577.76 \) or other provided values do not correspond correctly, so make sure to re-entry numbers or respect approximations.
Correct:
Feel free to take \( A = 660.04 \) or closest based on other insights, finalize choice based on context!