The ratio of volume of a cone to that of a cylinder if cylinder radius is reduced by 4 times and its height increased by 8 times of that of the cone, is -

The ratio of volume of a cone to that of a cylinder if cylinder radius is reduced by 4 times and its height increased by 8 times of that of the cone, is - Correct Answer 2:3

Ans. Let radius of the base and height of the cone be ‘r’ & ‘h’ respectively.

Then volume of cone = πr2h/3 For cylinder, radius is reduced by 4 times = r/4 And,  height is increased by 8 folds = 8h Volume of cylinder = πR2H = π(r/4)2 (8h) = (16/8)πr2h = πr2h/2 Ratio of volume of cone to volume of cylinder = (πr2h/3) : (πr2h/2) Or, Ratio = 2 : 3.

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