Problem 30
Question
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?
Step-by-Step Solution
Verified Answer
The volume of the larger cylinder is 16 times greater than that of the smaller cylinder.
1Step 1: 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.
2Step 2: 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.
3Step 3: 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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