SOLUTION: 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 14

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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.
Hope this is the correct section to post this question.
I have no idea how to solve this problem and don't understand that formula. Could somebody please explain how to solve this, or at least show me the steps so I can figure it out from there?
Thanks! Any help is appreciated.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
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.
:
Note that the volume of a cone is 1/3 the volume of a cylinder
r = radius, h = height
:
They give you the volume so we have:
= 144
:
It says,"height is one-fourth of the radius of the base.: therefore
h = .25r
replacing h with .25r in the formula we have
= 144
Now we only have one unknown, r
Multiply both sides by 3 to get rid of the fraction
= 3(144)
= 432
Which is
= 432
divide both sides by pi
=
= 137.5
Multiply both sides by 4 to get rid of .25
= 4(137.5)
= 550
r = , the cube root of both sides
use a calc, enter 550^(1/3)
r = 8.2 ft is the radius
:
:
See if that is right
r = 8.2, h = .25(8.2) = 2.05
:
v =
v = 144.3 close enough to confirm our solution of r = 8.2
:
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