Question

the radius of a cylinder decreases half of its original radius, keeping its height same.find the ratio of the volumes of new cylinder and the original cylinder

Answer 1

Let the volumes of original cylinder and new cylinder be V and V' respectively.

V=pie x r x r x h
V'=pie x 1/2r x 1/2r x h

=>V:V' =. 4:1
=>V':V = 1:4.

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Answer 2

Let r be radius of the cylinder

given radius is decreased by half

hence r becomes r/2

volume of original cylinder is πr²h

volume of new cylinder is π(r/2)²h

ratio of new to original cylinder will be [π(r/2)²h]/[πr²h]

from this we get ratio as 1:4