SOLUTION: The diameter of a cone at the top is 24 cm. When filled to a height of 10 cm, the column of water it holds is 30 pie cubic centimeters. Determine how much more water is needed to f
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Question 1030348: The diameter of a cone at the top is 24 cm. When filled to a height of 10 cm, the column of water it holds is 30 pie cubic centimeters. Determine how much more water is needed to fill the cone. Answer by mananth(16946) (Show Source):
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Volume of water at height of 10 cm = 30*pi cu.cm
let r be the radius at height 10 cm
V = (1/3) pi r^2h
30*pi = (1/3) *pi * r^2 *10
Simplify
r^2=9
r = 3 cm
(x+10)/12 = 10/3
x+10 =40
x=30 cm
Total height = 30+10 = 40cm
Volume of total cone = (1/3) pi *12^2 * 40
=6031.85 cu.cm
volume to be filled = 6031.85-30*pi
= 5937.6 cu cm
