Question

Two cones have their heights in the ratio 1:3 and radii in the ratio 3:1. what is the ratio of their volume
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Answer 1

Answer:

3:1

Step-by-step explanation:

Let heights be x and 3x respectively, while radii be 3y and y respectively.

Volume=1/3(πr²h)

Let the cones be Cone X and Cone Y respectively. Then,

ratio of volumes of Cone X to Cone Y is

$\frac{\frac{1}{3} \pi (3y)^2x}{\frac{1}{3}\pi y^2(3x) } \\\\=\frac{9xy^2}{3xy^2} \\\\=3:1$

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