Mathematics: 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

P (z less then or equal to -1.7)Step-by-step explanation:...

17. A hemisphere of lead of radius 7 cm is cast into - id17710082492, tacoursey1987p6xy9s

drew3vans34

14.02.2022

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

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