Question

Find the surface area of a cylinder with a base diameter length of 8 inches and a height of 10 inches. Use 3.14 for pi

Answer 1

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

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

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

First, find the radius \( r \). Given the diameter is 8 inches:

\[
r = \frac{\text{diameter}}{2} = \frac{8}{2} = 4 \text{ inches}
\]

Now, let's plug in the values: \( r = 4 \) inches and \( h = 10 \) inches. Using \( \pi \approx 3.14 \):

1. Calculate the area of the bases:

\[
2\pi r^2 = 2 \times 3.14 \times (4)^2 = 2 \times 3.14 \times 16
\]

Calculating \( 2 \times 3.14 \times 16 \):

\[
2 \times 3.14 = 6.28
\]

\[
6.28 \times 16 = 100.48
\]

So, the area of the bases is \( 100.48 \) square inches.

2. Calculate the lateral surface area:

\[
2\pi rh = 2 \times 3.14 \times 4 \times 10
\]

Calculating \( 2 \times 3.14 \times 4 \times 10 \):

\[
2 \times 3.14 = 6.28
\]

\[
6.28 \times 4 = 25.12
\]

\[
25.12 \times 10 = 251.2
\]

So, the lateral surface area is \( 251.2 \) square inches.

3. Now add the areas of the bases and the lateral surface area together:

\[
\text{Surface Area} = 100.48 + 251.2 = 351.68
\]

Thus, the surface area of the cylinder is:

\[
\boxed{351.68} \text{ square inches}
\]