Question

The volume of a cone is the same as that of the cylinder whose height is 9 cm and diameter 40 cm.Find the radius of the base of the cone if its height is 108 cm.

Answer 1

it is given that,
volume of cone= volume of cylinder
means, (1/3)×πr^2h=πr^2h
cylinder diameter=40, so that r=20cm
(1/3)×πr^2×108=π20×20×9
or r^2=20×20×9×3/108
or r^2=20×20/4
or r=√400/4
.•. r=10 cm answer.
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Answer 2

According to the question,

volume of cone= volume of cylinder. which means,

(1/3)×πr^2h=πr^2h

Given, cylinder diameter=40cm,

so r=20cm

(1/3)×πr^2×108=π20×20×9

or r^2=20×20×9×3/108

or r^2=20×20/4

or r=√400/4

.•. r=10 cm (answer)