Question

Find the surface area of the cylinder of 7 yd and 8 yd use 3.14 pi

Answer 1

To find the surface area of a cylinder, you can use the formula:

\[
\text{Surface Area} = 2\pi rh + 2\pi r^2
\]

where \( r \) is the radius of the base of the cylinder, and \( h \) is the height of the cylinder.

Given:
- Diameter = 7 yd, so the radius \( r = \frac{7}{2} = 3.5 \) yd
- Height \( h = 8 \) yd
- Using \( \pi \approx 3.14 \)

Now we can calculate the surface area step by step:

1. **Calculate the lateral surface area**:
\[
2\pi rh = 2 \times 3.14 \times 3.5 \times 8
\]
\[
= 2 \times 3.14 \times 3.5 \times 8 = 2 \times 3.14 \times 28
\]
\[
= 2 \times 87.92 = 175.84 \text{ yd}^2
\]

2. **Calculate the area of the top and bottom circles**:
\[
2\pi r^2 = 2 \times 3.14 \times (3.5)^2
\]
\[
= 2 \times 3.14 \times 12.25 = 2 \times 38.615 = 77.23 \text{ yd}^2
\]

3. **Total Surface Area**:
\[
\text{Surface Area} = 175.84 + 77.23 = 253.07 \text{ yd}^2
\]

Thus, the surface area of the cylinder is approximately \( 253.07 \text{ yd}^2 \).