Question

Calculate the surface area of the closed cylinder if the radius is 2 inches and the height is 5 inches.

image
A.
10π
inches
2

B.
20π
inches
2

C.
24π
inches
2

D.
28π
inches
2

Answer 1

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

\[
\text{Surface Area} = 2\pi r(h + r)
\]

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

Given:
- Radius \( r = 2 \) inches
- Height \( h = 5 \) inches

Now substituting the values into the formula:

\[
\text{Surface Area} = 2\pi (2)(5 + 2)
\]

Calculating inside the parentheses first:

\[
h + r = 5 + 2 = 7
\]

Now substituting that back into the formula:

\[
\text{Surface Area} = 2\pi (2)(7)
\]

Calculating \( 2 \times 2 \times 7 \):

\[
= 2\pi \times 14
\]
\[
= 28\pi \, \text{square inches}
\]

Therefore, the surface area of the closed cylinder is \( \boxed{28\pi} \) square inches.

The correct answer is D. \( 28\pi \) square inches.