Question

17. A hemisphere of lead of radius 7 cm is cast into a right circular cone of height 49 cm. Find

the radius of the base of the cone

Answer 1

`r = 3.74cm`

Explanation:

Given

Hemisphere

`Radius = 7cm`

Cone

`Height = 49m`

Required

Determine the radius of the cone

First, we calculate the volume (V1) of the hemisphere.

`V_1 = (2)/(3)\pi r^3`

Substitute 7 for r

`V_1 = (2)/(3)\pi * 7^3`

`V_1 = (2)/(3)\pi * 343`

`V_1 = (686)/(3)\pi`

Volume (V2) of a cone is:

`V_2 = (1)/(3)\pi r^2h`

Because the lead is cast into a cone, then they have the same volume.

So, we have:

`(686)/(3)\pi = (1)/(3)\pi r^2h`

`686 = r^2h`

Substitute 49 for h

`686 = r^2 * 49`

Divide both sides by 49

`r^2 = (686)/(49)`

`r^2 = 14`

`r = \sqrt{14`

`r = 3.74cm`

Hence, the radius of the cone is 3.74cm