Question 826849
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Hi, there--

THE PROBLEM:
The volume of a cone is given by the rule {{{V=(1/3)*pi*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 cubic cm and its radius at the widest point is 
{{{sqrt(12)}}} cm, find the height of the cone, expressing your answer in terms of {{{(pi)}}}.

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(12)}}} for r into the formula.
{{{V=(1/3)(pi)*r^2*h}}}
{{{(100)=(1/3)(pi)*(sqrt(12))^2*h}}}

Simplify. When you square the square root of 12 you get 12 because one operation undoes 
the other; 1/3 of 12 is 4.
{{{(100)=(1/3)(pi)*12*h}}}
{{{(100)=4*(pi)*h}}}

Solve for h. Divide both sides of the equation by {{{4*pi}}}.
{{{h = 100/(4*pi)}}}

Simplify. 100 divided by 4 is 25.
{{{h=25/(pi)}}}


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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