SOLUTION: A solid metal ball of radius 2 cm is melted and the metal obtained recast to form a solid right circular cone of radius 5 cm. Find the height of the cone.

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Question 386510: A solid metal ball of radius 2 cm is melted and the metal obtained recast to form a solid right circular cone of radius 5 cm. Find the height of the cone.
Found 2 solutions by Fombitz, mananth:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The volume of the metal remains the same.
For a sphere,
V%5Bs%5D=%284%2F3%29pi%2AR%5E3
V%5Bs%5D=%284%2F3%29pi%2A2%5E3
V%5Bs%5D=%2832%2F3%29pi
For a cone,
V%5Bc%5D=%28pi%2F3%29r%5E2%2Ah
V%5Bc%5D=%28%285%2Api%29%2F3%29r%5E2
.
.
.
V%5Bc%5D=V%5Bs%5D
%28%285%2Api%29%2F3%29r%5E2=%2832%2F3%29pi
5r%5E2=32
r%5E2=32%2F5
r=sqrt%2832%2F5%29
r=sqrt%28160%29%2F5
highlight%28r=%284%2F5%29sqrt%2810%29%29

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Volume V of ball = 4/3 * pi*2^3
= 33.5 cm^3
..
Volume V of cone = 1/3 *pi*r^2*h
33.5 = 1/3*pi*5^2*h
...
h=33.5*3/pi*25
h=1.28 cm
height = 1.28 cm
...
m.ananth@hotmail.ca