To correctly calculate the surface area of the cylinder again, let's follow the formula step by step, confirming the values.
The surface area \(A\) of a cylinder is given by the formula:
\[
A = 2\pi r(h + r)
\]
where:
- \( r = 7 \) yards (radius)
- \( h = 8 \) yards (height)
- \( \pi \approx 3.14 \)
Plugging in the values:
-
Calculate \( h + r \):
\[
h + r = 8 + 7 = 15
\]
-
Use the surface area formula:
\[
A = 2 \times 3.14 \times 7 \times 15
\]
-
Calculate:
- \( 2 \times 3.14 = 6.28 \)
- \( 6.28 \times 7 = 43.96 \)
- \( 43.96 \times 15 = 659.4 \) square yards
Since my previous calculations yielded 659.4 square yards and that still does not match the choices you provided, let's break down and check the surface area components separately:
The surface area also consists of:
- Lateral area = \( 2\pi rh \)
- Area of the top and bottom = \( 2\pi r^2 \)
Calculating these separately:
-
Lateral area:
\[
\text{Lateral Area} = 2 \times 3.14 \times 7 \times 8
\]
\[
= 2 \times 3.14 \times 56 = 352.32 \text{ square yards}
\]
-
Area of the top and bottom:
\[
\text{Area of Top and Bottom} = 2 \times 3.14 \times 7^2
\]
\[
= 2 \times 3.14 \times 49 = 307.76 \text{ square yards}
\]
-
Total Surface Area:
\[
\text{Total Surface Area} = 352.32 + 307.76 = 660.08 \text{ square yards}
\]
It appears there is consistent confusion with decimal calculations or rounding in earlier messages. The approximate possible rounded surfaces aren't matching your options. For clarity, none of the options you provided (577.76, 329.7, 252.77) were indicated in prior evaluations.
If only to select a correct response based on possible options, I'd lean towards averaging out errors, but mathematically, my calculations provide 660.08 square yards or something near.
If you'll need a choice of provided numbers, I cannot endorse a specific one due to significant discrepancy against calculations.
