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Chapter 2: Problem 30

A cylinder with radius 2 inches and height 3 inches has its radius quadrupled. 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 16 times greater than that of the smaller cylinder.

Step by step solution

01

Calculate Initial Volume

The volume of a cylinder is given by the formula \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height. Using the provided radius and height, calculate the initial volume.
02

Calculate New Volume

Quadruple the initial radius, then calculate the new volume for the larger cylinder using the same formula but with the quadrupled radius.
03

Find the Ratio

Divide the larger volume by the smaller volume to find out how many times greater the larger volume is compared to the smaller volume.

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