To find the surface area of a cylinder, we can 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,
- \( \pi \) is approximately 3.14.
Given:
- \( r = 7 \) yards
- \( h = 8 \) yards
Now, substitute the values into the formula:
-
Calculate the area of the two circular bases:
\[
2\pi r^2 = 2 \times 3.14 \times (7^2) = 2 \times 3.14 \times 49 = 6.28 \times 49 = 307.72 \text{ square yards}
\]
-
Calculate the area of the curved surface:
\[
2\pi rh = 2 \times 3.14 \times 7 \times 8 = 2 \times 3.14 \times 56 = 6.28 \times 56 = 351.68 \text{ square yards}
\]
-
Add both areas together:
\[
\text{Surface Area} = 307.72 + 351.68 = 659.4 \text{ square yards}
\]
None of the options given match this calculation, which suggests an error in the calculation of the individual areas. Let's examine the calculations again for accuracy.
Recalculating Areas
-
Area of the two circular bases:
\[
2\pi r^2 = 2 \times 3.14 \times (7^2) = 2 \times 3.14 \times 49 = 307.72 \text{ square yards}
\]
-
Area of the curved surface (Confirmation):
\[
2\pi rh = 2 \times 3.14 \times 7 \times 8 = 2 \times 3.14 \times 56 = 6.28 \times 56 = 351.68 \text{ square yards}
\]
-
Final Calculation of Total Surface Area:
Now add both calculated areas again:
\[
\text{Surface Area} = 307.72 + 351.68 = 659.4 \text{ square yards}
\]
Conclusion
The surface area calculation yields approximately 659.4 square yards, however, this isn't one of the provided responses. Therefore, there may be an inconsistency in the options offered.
To choose the closest answer based on area (but keeping in mind the calculations provided above), none of the options seem to reflect the computed surface area correctly.
If we would have to pick an option regardless, it's best to clarify with a precise option or recalculate based on the correct values mentioned.
