SOLUTION: Hello! The problem I have is that I need to "find the volume of a cone slant height of which is nine times the radius and the height of 12√5 units." Either I am not sure ho

Algebra ->  Volume -> SOLUTION: Hello! The problem I have is that I need to "find the volume of a cone slant height of which is nine times the radius and the height of 12√5 units." Either I am not sure ho      Log On


   

Question 1132645: Hello!
The problem I have is that I need to "find the volume of a cone slant height of which is nine times the radius and the height of 12√5 units."
Either I am not sure how to write the answer, or I don't understand what is being asked, or I am doing it wrong. I tried 2880π√(5), and 4π√(5)r^2, but neither of those worked.
Thanks for helping!
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

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given:
slant height s=9r+
the height h=12sqrt%285%29
V=%28pir%5E2%2Ah%29%2F3

from right triangle, slant height is hypotenuse, the radius and the height are legs

r=sqrt%28s%5E2-h%5E2%29

r=sqrt%28%289r%29%5E2-%2812sqrt%285%29%29%5E2%29

r=sqrt%2881r%5E2-144%285%29%29

r=sqrt%2881r%5E2-720%29.....square both sides

r%5E2=81r%5E2-720

720=81r%5E2-r%5E2

720=80r%5E2

r%5E2=720%2F80

r%5E2=9

r=3

=>slant height s=9r=9%2A3=27+

then
V=%28pi%2A3%5E2%2A12sqrt%285%29%29%2F3

V=%28pi%2A3%5Ecross%282%29%2A12sqrt%285%29%29%2Fcross%283%29

V=+pi%2A3%2A12sqrt%285%29

V=+pi%2A36sqrt%285%29-> exact solution

approximately:
V=+252.89