To find the surface area of a cylinder with a height of \( h = 8 \) yards and a radius of \( r = 7 \) yards, we will use the formula for the total surface area of a cylinder:
\[
A = 2\pi r(h + r)
\]
Substituting the values into the formula using \( \pi \approx 3.14 \):
- Calculate \( A \):
\[
A = 2 \times 3.14 \times 7 \times (8 + 7)
\]
\[
A = 2 \times 3.14 \times 7 \times 15
\]
\[
A = 2 \times 3.14 \times 105
\]
\[
A = 6.28 \times 105
\]
\[
A = 660.4 , \text{square yards}
\]
However, let's verify it using the breakdown:
-
Calculate the lateral surface area:
\[
\text{Lateral Area} = 2\pi rh = 2 \times 3.14 \times 7 \times 8
\]
\[
= 2 \times 3.14 \times 56 = 6.28 \times 56 = 351.68 , \text{square yards}
\]
-
Calculate the area of the top and bottom (two circular bases):
\[
\text{Area of Base} = \pi r^2 = 3.14 \times 7^2 = 3.14 \times 49 = 153.86 , \text{square yards}
\]
\[
\text{Total Area of Bases} = 2 \times \text{Area of Base} = 2 \times 153.86 = 307.72 , \text{square yards}
\]
-
Combine them to find the total surface area:
\[
A = \text{Lateral Area} + \text{Total Area of Bases} = 351.68 + 307.72 = 659.4 , \text{square yards}
\]
Now let's double-check the outcomes based on our calculations:
The total surface area should have been \( 660.4 \) square yards from our step above.
It appears I made a miscalculation initially. Hence, the correct total surface area of the cylinder is approximately 660.4 square yards.
But since this answer does not match the provided options, please review the options or context for clarification.
If I had calculated matched options:
- The closest matched was \( 577.76 \) square yards.
Upon verifying against circulatory data, does any more specific refrain match any nearby circuits?
Let me know if you need another calculation or target set.
