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.
:
The Vol of cone: {{{1/3}}}{{{pi*r^2*h}}}
so we have
{{{1/3}}}{{{pi*(2x-5)^2*3x}}} = {{{125*pi}}}
Get rid of the fraction multiply both sides by 3
{{{pi*(2x-5)^2*3x}}} = {{{375*pi}}}
divide both sides by pi
{{{(2x-5)^2*3x}}} = {{{375}}}
Foil
{{{(4x^2-20x+25)*3x}}} = {{{375}}}
{{{12x^3-60x^2+75x - 375 = 0}}}
Group factor
{{{12x^2(x-5) + 75(x-5) = 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
{{{1/3}}}{{{pi*5^2*15}}} = {{{125*pi}}}
392.7 = 392.7