The radii of the base of a cylinder and a cone are in the ratio 3 : 4. If they have their heights in the ratio 2 : 3, the ratio between their volumes is

(a) 9 : 8 (b) 3 : 4 (c) 8 : 9 (d) 4 : 3

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Solution

Let R be the radius of the cylinder and r be the radius of the cone. Similarly, let H be the height of the cylinder and h be the height of the cone. R/r = 3/4 H/h = 2/3 Ratio:

$fraction numerator v o l u m e space o f space c y l i d e r over denominator v o l u m e space o f space c o n e end fraction equals fraction numerator pi R squared H over denominator begin display style 1 third pi r squared h end style end fraction$

= $fraction numerator 3 cross times 3 cross times 2 over denominator begin display style 1 third cross times 4 cross times 4 cross times 3 end style end fraction$

= (18) / (16)

= 9/8

Therefore, ratio of their volumes is 9:8.

Ans) a] 9:8 is the correct option.

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