Question

If the ratios of the volumes of two cones are 216:64, and the larger cone's height is 20in, what is the height of the smaller cone to the nearest inch?

Answer 1

13 inches (to nearest inch)

Explanation:

if volumes are in ratio 216:64, then lengths/heights must be in ratio

∛216: ∛64

= 6:4.

this can be simplified to 3:2.

3/2 = 1.5.

that means the height of larger cone is 1.5 times taller than height of the smaller cone.

let's call height of smaller cone d.

20 = 1.5d

d = 20/1.5

= 13.33

= 13 inches (to nearest inch)