SOLUTION: A cylinder has a volume of 24 cm^3. The height of a cone with the same radius is two times the height of the cylinder. What is the volume of the cone? Thank you

Question 1072569: A cylinder has a volume of 24 cm^3. The height of a cone with the same radius is two times the height of the cylinder. What is the volume of the cone? Thank you
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Cylinder is pi*r^2*h=24; therefore h=24/pi*r^2 and 2h=48/pi*r^2
Cone is (1/3)pi*r^3*2h.
The ratio of the two is 3/2r.
If the cylinder is 24, then 24/x=3/2r
3x=48r
x=16r, the volume of the cone.
Check with numbers where radius is 3 and height 4
volume of cylinder is pi*9*4=36 pi
volume of cone is (1/3)*pi*27*8=72pi
The ratio of these two is 1/2, and with a ratio of 3/2r, with a radius of 3, the ratio is indeed 1/2.
Therefore, the cone's volume is 48 cm^3 ANSWER
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