To find the surface area of a cylinder, we 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.
From your question, it looks like the width you provided (7 yards) is the diameter of the cylinder. Therefore, the radius \( r \) is half of the diameter:
\[ r = \frac{\text{diameter}}{2} = \frac{7 , \text{yards}}{2} = 3.5 , \text{yards} \]
The height \( h \) is given as 8 yards.
Now, substituting \( r \) and \( h \) into the surface area formula:
- Calculate \( 2\pi r^2 \):
\[ 2\pi r^2 = 2 \times 3.14 \times (3.5)^2 \] \[ (3.5)^2 = 12.25 \] \[ 2 \times 3.14 \times 12.25 = 76.505 , \text{square yards} \]
- Calculate \( 2\pi rh \):
\[ 2\pi rh = 2 \times 3.14 \times 3.5 \times 8 \] \[ 2 \times 3.14 \times 3.5 = 21.98 \] \[ 21.98 \times 8 = 175.84 , \text{square yards} \]
- Add the two areas together:
\[ \text{Surface Area} = 76.505 + 175.84 = 252.345 , \text{square yards} \]
Thus, the surface area of the cylinder is approximately 252.77 square yards.
So the correct response from the options you provided is 252.77 square yards.
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