Question

Find the surface area of a cylinder with a base diameter length of 8 in. and a
height of 10 in. Use n= 3.14. (1 point)

Answer 1

To calculate 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,
- \( h \) is the height of the cylinder,
- \( \pi \) is a constant (approximately 3.14 in this case).

Given:
- The diameter of the base is 8 inches, so the radius \( r \) is half of the diameter:
\[
r = \frac{8}{2} = 4 \text{ inches}
\]
- The height \( h \) is 10 inches.

Now substitute \( r = 4 \) and \( h = 10 \) into the surface area formula:

1. Calculate the lateral surface area:
\[
2\pi rh = 2 \times 3.14 \times 4 \times 10
\]
\[
= 2 \times 3.14 \times 40 = 8 \times 3.14 = 25.12 \times 10 = 314 \text{ square inches}
\]

2. Calculate the area of the two bases:
\[
2\pi r^2 = 2 \times 3.14 \times (4^2) = 2 \times 3.14 \times 16
\]
\[
= 6.28 \times 16 = 100.48 \text{ square inches}
\]

3. Add both areas together:
\[
\text{Total Surface Area} = 314 + 100.48 = 414.48 \text{ square inches}
\]

So, the surface area of the cylinder is approximately **414.48 square inches**.