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

Question

asked Apr 5, 2021 146k views

1 Answer

Jgorostegui · Answer 1 · 2021-04-09T13:15:59+0000

Answer:

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