Question

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

Answer 1

Answer:

$r = 3.74cm$

Step-by-step explanation:

Given

Hemisphere

$Radius = 7cm$

Cone

$Height = 49m$

Required

Determine the radius of the cone

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

$V_1 = \frac{2}{3}\pi r^3$

Substitute 7 for r

$V_1 = \frac{2}{3}\pi * 7^3$

$V_1 = \frac{2}{3}\pi * 343$

$V_1 = \frac{686}{3}\pi$

Volume (V2) of a cone is:

$V_2 = \frac{1}{3}\pi r^2h$

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

So, we have:

$\frac{686}{3}\pi = \frac{1}{3}\pi r^2h$

$686 = r^2h$

Substitute 49 for h

$686 = r^2 * 49$

Divide both sides by 49

$r^2 = \frac{686}{49}$

$r^2 = 14$

$r = \sqrt{14$

$r = 3.74cm$

Hence, the radius of the cone is 3.74cm