Question 292216
As sand is poured from a chute, it forms a right circular cone whose height is
 one-fourth of the radius of the base.
 What is the radius of the base when the cone has a volume of 144 cubic feet?
 You may use the formula V=1/3(pi)r^2h for the volume of a right circular
 cone with a radius r and height h.
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Note that the volume of a cone is 1/3 the volume of a cylinder
r = radius, h = height
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They give you the volume so we have:
{{{(1/3)*pi*r^2*h}}} = 144
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It says,"height is one-fourth of the radius of the base.: therefore
h = .25r
replacing h with .25r in the formula we have
{{{(1/3)*pi*r^2*.25r}}} = 144
Now we only have one unknown, r
Multiply both sides by 3 to get rid of the fraction
{{{pi*r^2*.25r}}} = 3(144)
{{{pi*r^2*.25r}}} = 432
Which is
{{{pi*.25r^3}}} = 432
divide both sides by pi
{{{.25r^3}}} = {{{432/pi}}}
{{{.25r^3}}} = 137.5
Multiply both sides by 4 to get rid of .25
{{{r^3}}} = 4(137.5)
{{{r^3}}} = 550
r = {{{550^(1/3)}}}, the cube root of both sides
use a calc, enter 550^(1/3)
r = 8.2 ft is the radius
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See if that is right
r = 8.2, h = .25(8.2) = 2.05
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v = {{{(1/3)*pi*8.2^2*2.05}}} 
v = 144.3 close enough to confirm our solution of r = 8.2
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