Question

Find the surface area of a cylinder with the diameter of 12 inches and a height of 10 inches. Use the approximation of 3.14 for pi.

Answer 1

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

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

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

First, we need to find the radius. Since the diameter of the cylinder is 12 inches, the radius \( r \) is half of the diameter:

\[
r = \frac{12}{2} = 6 \text{ inches}
\]

Given that the height \( h \) of the cylinder is 10 inches, we can now substitute the values into the surface area formula. Using \( \pi \approx 3.14 \):

1. Calculate the area of the two circular bases:

\[
2\pi r^2 = 2 \times 3.14 \times (6)^2
\]
\[
= 2 \times 3.14 \times 36
\]
\[
= 2 \times 113.04 = 226.08 \text{ square inches}
\]

2. Calculate the area of the side (lateral surface area):

\[
2\pi rh = 2 \times 3.14 \times 6 \times 10
\]
\[
= 2 \times 3.14 \times 60
\]
\[
= 2 \times 188.4 = 376.8 \text{ square inches}
\]

3. Now, add the two areas together to get the total surface area:

\[
\text{Surface Area} = 226.08 + 376.8 = 602.88 \text{ square inches}
\]

Thus, the surface area of the cylinder is:

\[
\boxed{602.88} \text{ square inches}
\]