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Chapter 10: Problem 37

A cylinder with radius 3 inches and height 4 inches has its radius tripled. How many times greater is the volume of the larger cylinder than the smaller cylinder?

Short Answer

Expert verified
The volume of the larger cylinder is 9 times greater than the volume of the smaller cylinder.

Step by step solution

01

Calculate the volume of the smaller cylinder

Apply the formula for the volume of a cylinder, where \( r = 3 \) inches and \( h = 4 \) inches: \( V_{small} = \pi \cdot (3^2) \cdot 4 \)
02

Calculate the volume of the larger cylinder

The radius of the larger cylinder is triple the radius of the smaller. Therefore, \( r = 3 \times 3 = 9 \) inches. So apply the formula for the volume of a cylinder again, where \( r = 9 \) inches and \( h = 4 \) inches: \( V_{large} = \pi \cdot (9^2) \cdot 4 \)
03

Determine how many times greater the volume of the larger cylinder is

To find out how many times greater the volume of the larger cylinder is, we can divide the volume of the larger cylinder by the volume of the smaller cylinder: \( ratio = V_{large} / V_{small}\)

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