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

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--

THE PROBLEM:
The volume of a cone is given by the rule V=%281%2F3%29%2Api%2Ar%5E2%2Ah, 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 
sqrt%2812%29 cm, find the height of the cone, expressing your answer in terms of %28pi%29.

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 sqrt%2812%29 for r into the formula.
V=%281%2F3%29%28pi%29%2Ar%5E2%2Ah
%28100%29=%281%2F3%29%28pi%29%2A%28sqrt%2812%29%29%5E2%2Ah

Simplify. When you square the square root of 12 you get 12 because one operation undoes 
the other; 1/3 of 12 is 4.
%28100%29=%281%2F3%29%28pi%29%2A12%2Ah
%28100%29=4%2A%28pi%29%2Ah

Solve for h. Divide both sides of the equation by 4%2Api.
h+=+100%2F%284%2Api%29

Simplify. 100 divided by 4 is 25.
h=25%2F%28pi%29


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