To find the surface area of a cylinder, you can use the formula:
\[ \text{Surface Area} = 2\pi r(h + r) \]
Where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.
From the information given:
- The height \( h = 8 \) yards,
- The diameter of the cylinder is \( 7 \) yards, so the radius \( r = \frac{7}{2} = 3.5 \) yards.
Now, substituting the values into the formula:
\[ \text{Surface Area} = 2 \cdot 3.14 \cdot 3.5 \cdot (8 + 3.5) \]
Calculating \( (8 + 3.5) \):
\[ 8 + 3.5 = 11.5 \]
Now plug this back into the formula:
\[ \text{Surface Area} = 2 \cdot 3.14 \cdot 3.5 \cdot 11.5 \]
Calculating \( 2 \cdot 3.14 \cdot 3.5 \):
\[ 2 \cdot 3.14 = 6.28 \] \[ 6.28 \cdot 3.5 = 21.98 \]
Now, multiply by \( 11.5 \):
\[ 21.98 \cdot 11.5 \approx 253.77 \]
Thus, the surface area of the cylinder is approximately 253.77 square yards.
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