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.

First, we need to find the radius. The diameter of the base is given as 8 inches, so the radius \( r \) is:

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

Now, the height \( h \) is given as 10 inches. Now we can substitute \( r \) and \( h \) into the surface area formula.

Calculating the area of the two bases:

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

Calculating the lateral surface area:

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

Now, adding the areas together to find the total surface area:

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

So, the surface area of the cylinder is

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