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)
in.2

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.

Given a diameter of 8 inches, we can find the radius:

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

We are also given the height \( h = 10 \, \text{in} \).

Now, substitute the values of \( r \) and \( h \) into the surface area formula. First, calculate the area of the two circular bases:

\[
2\pi r^2 = 2 \times 3.14 \times (4 \, \text{in})^2 = 2 \times 3.14 \times 16 \, \text{in}^2 = 2 \times 50.24 \, \text{in}^2 = 100.48 \, \text{in}^2
\]

Next, calculate the lateral surface area:

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

Now, add the two areas together for the total surface area:

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

Therefore, the surface area of the cylinder is

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