Question

find the surface area of the cylinder. the diameter is 7 yds and the height is 8 yds

Answer 1

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, \( h \) is the height, and \( \pi \) is approximately 3.14.

1. **Find the radius**: Since the diameter is given as 7 yards, the radius \( r \) is half of the diameter.
\[
r = \frac{7 \text{ yd}}{2} = 3.5 \text{ yd}
\]

2. **Use the height**: The height \( h \) is given as 8 yards.

3. **Substitute the values into the formula**:
\[
\text{Surface Area} = 2\pi (3.5 \text{ yd})(8 \text{ yd} + 3.5 \text{ yd})
\]
\[
= 2\pi (3.5 \text{ yd})(11.5 \text{ yd})
\]
\[
= 2\pi (40.25 \text{ yd}^2)
\]
\[
= 80.5\pi \text{ yd}^2
\]

4. **Calculate the approximate value** (using \( \pi \approx 3.14 \)):
\[
\text{Surface Area} \approx 80.5 \times 3.14 \approx 252.07 \text{ yd}^2
\]

Thus, the surface area of the cylinder is approximately \( 252.07 \text{ yd}^2 \).