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)

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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