Question 9 of 20

Use the image to answer the question.

The cylinders shown below are similar.

Two cylinders are shown side by side. The first cylinder has a height of 3 inches and a radius of 1 inch. The second cylinder has a height of 9 inches and a radius of 3 inches.

What is the ratio of their surface areas?

A.
1
27
B.
3
27
C.
1
9
D.
1
3

1 answer

The surface area of a cylinder can be found using the formula A = 2πr² + 2πrh, where r is the radius and h is the height.

For the first cylinder, A = 2π(1²) + 2π(1)(3) = 2π + 6π = 8π.

For the second cylinder, A = 2π(3²) + 2π(3)(9) = 18π + 54π = 72π.

The ratio of their surface areas can be found by dividing the larger surface area by the smaller surface area:

72π / 8π = 9

Therefore, the ratio of their surface areas is 9.

Answer: C. 1/9.