Question

Caroline draws the cylinder shown here and calculates the volume. She then draws a second cylinder in which the dimensions are tripled. What is the relationship between the volumes of the two cylinders? A) The volume of the second cylinder is 3 times that of the first cylinder. B) The volume of the second cylinder is 8 times that of the first cylinder. C) The volume of the second cylinder is 9 times that of the first cylinder. D) The volume of the second cylinder is 27 times that of the first cylind

Answer 1

D) The volume of the second cylinder is 27 times that of the first cylinder

Explanation:

Let r, h and V represent the radius, height and volume of the cylinder.

When the dimensions are tripled, 3r, 3h and V1 represent the radius, height and volume of the cylinder.

We want to find the relationship between V and V1

Volume of a cylinder:

V = πr^2 h

When tripled;

V1 = π(3r)^2 × 3h = π(9r^2)×3h

V1 = 27πr^2 h

So,

V1/V = (27πr^2 h)/(πr^2 h)

V1/V = 27

Therefore, when the dimensions are tripled the volume is 27 times.

The volume of the second cylinder is 27 times that of the first cylinder