Question 617507
f the volume of a cone is 168pi inches^3 and its altitude is 14 inches, what is the radius of the cone?
:
The volume of a cone formula: V = {{{1/3}}}*{{{pi*r^2*h}}}
Given: v = 168pi, h = 14, find r
{{{1/3}}}*{{{pi*r^2*14}}} = {{{168*pi}}}
divide both sides by pi
{{{1/3}}}*{{{r^2*14}}} = 168
Multiply both sides by 3
{{{r^2*14}}} = 504
divide both sides by 14
r^2 = {{{504/(14)}}}
:
r^2 = 36
r = {{{sqrt(36)}}}
r = 6 inches is the radius
:
:
Check this on your calc:
forget pi, it's on both sides of the equation.
 enter {{{1/3}}}*{{{6^2*14}}} results: 168