Question

please solve the following question-
The base radii of two right circular cones of the same height are in the ratio 3:5. Find the ratio of their volumes.

Answer 1

ratio of radii are 3:5

let radius of 1st cone(r1) = 3x

radius of 2nd cone(r2) = 5x

volume of a cone = π*r^2*h

ratio of their volume = 3*π*(3x)^2*h/3*π*(5x)^2*h (because ratio of radii = 3:5 and ) (heights are equal)

= 9x^2/25x^2

= 9/25

ratio of their volumes are 9:25

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