The volume of a cylinder is 96 inches cubed. The height of a cylinder is 3 times the height of the first cylinder and the radius of its base is 1/4 times the radius of the first cylinder. What is the volume of the second cylinder?

96=r^2*pi*h

96=pi*3h*(1/4)(1/2)base, since the height is 3 times taller, and base/2=radius, so (1/2) of a base that is (1/4) as large.

96=pi*3h*1/8r^2

96=3/8*pi*h*r^2

Do that to both sides, and you get:

96*(3/8)=3/8*pi*h*r^2

Or, the new volume is 36 inches cubed.

I misread the question. It should be:

96=pi*3h*1/4r^2. They didn't restate the base. The correct answer is:

96=3/4*pi*h*r^2

Or 96*3/4=24*3=

72 inches cubed.

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