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 and \( h \) is the height of the cylinder.
Given:
- The diameter of the cylinder is \( 7 \) yd, so the radius \( r \) is half of that: \[ r = \frac{7}{2} = 3.5 \text{ yd} \]
- The height \( h \) of the cylinder is \( 8 \) yd.
Now, plug in the values into the surface area formula using \( \pi \approx 3.14 \):
\[ \text{Surface Area} = 2 \times 3.14 \times 3.5(8 + 3.5) \]
Now calculate \( (8 + 3.5) \):
\[ 8 + 3.5 = 11.5 \]
Now substitute back into the surface area equation:
\[ \text{Surface Area} = 2 \times 3.14 \times 3.5 \times 11.5 \]
Calculating step by step:
- Calculate \( 2 \times 3.14 = 6.28 \)
- Then calculate \( 6.28 \times 3.5 = 21.98 \)
- Finally, calculate \( 21.98 \times 11.5 \approx 252.77 \)
Thus, the surface area of the cylinder is approximately:
\[ \text{Surface Area} \approx 252.77 \text{ square yards} \]