SOLUTION: The volume of ice-cream in the cone is half the volume of the con. The cone has a 3cm radius and 14cm height. What is the depth of the ice-cream correct to two decimal place?

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Question 1041491: The volume of ice-cream in the cone is half the volume of the con. The cone has a 3cm radius and 14cm height. What is the depth of the ice-cream correct to two decimal place?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The volume of a cone is,
V=%28pi%2F3%29r%5E2%2Ah
In this case,
V=%28pi%2F3%29%283%29%5E2%2A14
V=42pi
So,
V%5BIC%5D=42pi%2F2=21pi
There is also a relationship between the radius and the height of the ice cream within the cone.
When r=3, h=14 and when r=0, h=0
So then,
r%5BIC%5D=%283%2F14%29h%5BIC%5D
So calculating the ice cream volume,
%28pi%2F3%29r%5BIC%5D%5E2%2Ah%5BIC%5D=1pi
Substituting,
%28pi%2F3%29%283%2F14%29%5E2%2Ah%5BIC%5D%5E2%2Ah%5BIC%5D=21pi
h%5BIC%5D%5E3=1372
h%5BIC%5D=%281372%29%5E%281%2F3%29
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I leave it to you to get the decimal equivalent of the cube root.