SOLUTION: A right circular cone has a base radius of 2x-5 and a height of 3x. The cone has a volume of 125pi cubic units. Find the possible value(s) of x.

Algebra ->  Rational-functions -> SOLUTION: A right circular cone has a base radius of 2x-5 and a height of 3x. The cone has a volume of 125pi cubic units. Find the possible value(s) of x.      Log On


   

Question 834353: A right circular cone has a base radius of 2x-5 and a height of 3x. The cone has a volume of 125pi cubic units. Find the possible value(s) of x.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A right circular cone has a base radius of 2x-5 and a height of 3x.
The cone has a volume of 125pi cubic units.
Find the possible value(s) of x.
:
The Vol of cone: 1%2F3pi%2Ar%5E2%2Ah
so we have
1%2F3pi%2A%282x-5%29%5E2%2A3x = 125%2Api
Get rid of the fraction multiply both sides by 3
pi%2A%282x-5%29%5E2%2A3x = 375%2Api
divide both sides by pi
%282x-5%29%5E2%2A3x = 375
Foil
%284x%5E2-20x%2B25%29%2A3x = 375
12x%5E3-60x%5E2%2B75x+-+375+=+0
Group factor
12x%5E2%28x-5%29+%2B+75%28x-5%29+=+0
Factor (x-5)
(x-5)(12x^2+75) = 0
one positive solution
x = 5
;
:
See if this works out
r = 2(5) - 5
r = 5
h = 3*5 = 15
Use a calc
1%2F3pi%2A5%5E2%2A15 = 125%2Api
392.7 = 392.7