To find the surface area of a cylinder, we can use the formula:
\[ \text{Surface Area} = A_{\text{top}} + A_{\text{bottom}} + A_{\text{side}} \]
Where:
- \( A_{\text{top}} \) and \( A_{\text{bottom}} \) are the areas of the top and bottom circles.
- \( A_{\text{side}} \) is the area of the side (lateral area).
- Calculate the area of the top and bottom circles:
- The area of a circle is given by \( A = \pi r^2 \).
- Here, the radius \( r \) is 14 yd.
\[ A_{\text{top}} = A_{\text{bottom}} = \pi r^2 = \pi (14)^2 = \pi (196) \approx 3.14 \times 196 \]
Calculating that:
\[ A_{\text{top}} \approx 3.14 \times 196 \approx 615.44 , \text{square yards} \]
So, \( A_{\text{top}} + A_{\text{bottom}} = 615.44 + 615.44 = 1230.88 , \text{square yards} \).
- Calculate the lateral area:
- The lateral area of a cylinder is given by \( A_{\text{side}} = 2 \pi r h \).
- The height \( h \) is 8 yd.
\[ A_{\text{side}} = 2 \pi r h = 2 \pi (14)(8) = 2 \pi (112) \approx 2 \times 3.14 \times 112 \]
Calculating that:
\[ A_{\text{side}} \approx 2 \times 3.14 \times 112 \approx 703.68 , \text{square yards} \]
- Combine all the areas to find the total surface area:
\[ \text{Surface Area} = A_{\text{top}} + A_{\text{bottom}} + A_{\text{side}} = 1230.88 + 703.68 \]
Calculating that:
\[ \text{Surface Area} \approx 1230.88 + 703.68 \approx 1934.56 , \text{square yards} \]
Rounding to the nearest hundredth, the surface area of the cylinder is:
\[ \boxed{1934.56} , \text{square yards} \]
1 answer