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If the radius of the base of a right circular cylinder is halved , keeping the height same , what is the ratio of the volume of the reduce cylinder to that of the original.

Answers (1)

D Deependra Verma

Solution : Let r be the radius of the base and $h$ be the height of the given cylinder .

Then , radius of the base and the height of the reduced cylinder are $fracr2$ and $h$ respectively .

Let $V_1$ and $V_2$ be the volumes of the given cylinder and reduced cylinder respectively . Then,

$V_1= pi r^2h$ cubic units and , $V_2= pi (fracr2)^2h =fracpi4r^2h$ cubic units

$Rightarrow$ $fracV_1V_2=fracpi r^2hpi (fracr^24)h=4Rightarrow fracV_2V_1=frac14Rightarrow V_2:V_1=1:4$

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