Question

two cones have their height in ratio 1:3 and the radii of their bases in the ratio 3:1. show that there volume are in the ratio 3:1

Answer 1

Answer:

Step-by-step explanation:

Ratio of height-1:3

So let the heights of the cones be X and 3X.

Ratio of radii-3:1

So let the radii of the cones be 3Y and Y.

Cone-1  : Let the volume be v. Radius is 3Y and Height is X.

∴v=1/3×π×3Y×3Y×X

=3πXY²

Cone-2 : Let the volume be V. The radius is Y and the height is 3X.

∴V=1/3×π×Y×Y×3X

V=πXY².

The ratio of the volumes of two cone is v/V.

v/V=3πXY²/πXY²=3:1

∴v/V=3:1

Hence proved.