SOLUTION: The volume of a cone is given by the rule V=1/3pie*R^2*h, where r is the radius of the widest part of the cone and h is the vertical height of the cone. Given that the volume of a

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Question 826849: The volume of a cone is given by the rule V=1/3pie*R^2*h, where r is the radius of the widest part of the cone and h is the vertical height of the cone. Given that the volume of a cone is 100 cm3 and its radius at the widest point is sqrt12 cm, find the height of the cone, expressing your answer in terms of π.
Answer by math-vortex(648)   (Show Source): You can put this solution on YOUR website!
Hi, there--

THE PROBLEM:
The volume of a cone is given by the rule , where r is the radius of the 
widest part of the cone and h is the vertical height of the cone. 

Given that the volume of a cone is 100 cubic cm and its radius at the widest point is 
 cm, find the height of the cone, expressing your answer in terms of .

A SOLUTION:
Begin with the formula for the volume of a cone. Check that all measurements are in terms of 
cm, for length, or cubic cm, for volume. (They are.)

Substitute 100 cubic cm for V and  for r into the formula.



Simplify. When you square the square root of 12 you get 12 because one operation undoes 
the other; 1/3 of 12 is 4.



Solve for h. Divide both sides of the equation by .


Simplify. 100 divided by 4 is 25.



Hope this helps! Feel free to email if you have any questions about the solution.

Good luck with your math,

Mrs. F
math.in.the.vortex@gmail.com

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