Question

the radii of the base of a cylinder and a cone of same height are in the ratio 2:3 the ratio of their volume is​

Answer 1

The radii of bases of the cylinder and a cone are in the ratio 3:4 and their heights are in the ratio 2:3. The ratio between the volume of the cylinder to that of the cone is :

ANSWER :

Let r be radius of base of the cylinder and R be the radius of the base of the cone.

R/r = 3/4

Let h be the height of the cylinder and H be the height of the cone.

H/h = 2/3

∴ Volume of cylinder / Volume of cone

= πr^2h / 1/3 πR^2H

= 3 × ( r / R )^2 × ( h / H )

= 3 ×( 3 / 4)^2 × ( 2 / 3 )

= 3 × ( 9 / 8 ) × ( 2 / 3 )

= 9 / 8

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