Two cones have their heights in the ratio 1:3 and the radii of their b

1.	Two cones have their heights in the ratio 1:3 and the radii of their bases in the ratio 3:1. Show that their volumes are in the ratio 3:1.
Answer» Consider the heights as h and 3h and radii as 3r and r So we get V₁ = 1/3 π (3r) ²h and V₂ = 1/3 πr² × 3h By dividing both we get V₁/ V₂ = (1/3 π (3r) ²h)/ (1/3 πr² × 3h) On further calculation V₁/ V₂ = 3/1 It can be written as V₁:V₂ = 3:1 Therefore, it is proved that their volumes are in the ratio 3:1.

Two cones have their heights in the ratio 1:3 and the radii of their bases in the ratio 3:1. Show that their volumes are in the ratio 3:1.

Answer»

Consider the heights as h and 3h and radii as 3r and r

So we get

V₁ = 1/3 π (3r) ²h and V₂ = 1/3 πr² × 3h

By dividing both we get

V₁/ V₂ = (1/3 π (3r) ²h)/ (1/3 πr² × 3h)

On further calculation

V₁/ V₂ = 3/1

It can be written as

V₁:V₂ = 3:1

Therefore, it is proved that their volumes are in the ratio 3:1.