A cylinder has a volume of $1296 c u b i c i n c h e s$ . If you divide the radius of the cylinder by $12$ . What is the volume (in cubic inches) of the smaller cylinder?

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Solution

Use the relationship between Volume and radius of a cylinder
The formula for the volume of cylinder is given by ${πr}^{2} h$ where $r$ and $h$ are the radius and height of the cylinder respectively.
Since, Volume is directly proportional to the product of the square of radius and its height.
Therefore, when radius is divided by $12$ and height remains same, volume gets divided by ${(12)}^{2} = 144$
Volume of smaller cylinder $= \frac{1296}{144} = 9$
Hence, Volume of smaller cylinder is $9$ cubic inches.

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A cylinder has a volume of 1296cubicinches. If you divide the radius of the cylinder by 12. What is the volume (in cubic inches) of the smaller cylinder?

A cylinder has a volume of $1296 c u b i c i n c h e s$ . If you divide the radius of the cylinder by $12$ . What is the volume (in cubic inches) of the smaller cylinder?