Question

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

Answer 1

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

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

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

1. First, determine the radius \( r \) from the diameter. The diameter is given as 8 inches, so:

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

2. Now, using the given height \( h = 10 \) in. and \( \pi = 3.14 \), we can plug in the values into the surface area formula:

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

Calculating \( 2\pi r^2 \):

\[
2\pi r^2 = 2 \times 3.14 \times (4 \text{ in})^2
\]
\[
= 2 \times 3.14 \times 16 \text{ in}^2
\]
\[
= 2 \times 3.14 \times 16 = 100.48 \text{ in}^2
\]

Now calculating \( 2\pi rh \):

\[
2\pi rh = 2 \times 3.14 \times 4 \text{ in} \times 10 \text{ in}
\]
\[
= 2 \times 3.14 \times 40 \text{ in}^2
\]
\[
= 2 \times 125.6 = 251.2 \text{ in}^2
\]

3. Finally, add the two areas to find the total surface area:

\[
\text{Surface Area} = 100.48 \text{ in}^2 + 251.2 \text{ in}^2
\]
\[
= 351.68 \text{ in}^2
\]

Thus, the surface area of the cylinder is:

\[
\boxed{351.68} \text{ in}^2
\]