SOLUTION: a right circular cone has an altitude of 18 inches and a radius of 8 inches and is 1/4 filled with water. solve the height of the water

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Question 1085829: a right circular cone has an altitude of 18 inches and a radius of 8 inches and is 1/4 filled with water. solve the height of the water
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
If one draws a cone with some water in it, the original radius, 8, and the original height, 18, 8/18, are proportional to the radius of the water level r1 and the height of the water level h1 (similar triangles)
Volume of the cone is (1/3)*pi*r^2*h=(1/3)*pi*64*18=384 pi
a quarter full is 96 pi in^3
the equation of the cone with water only is V=96*pi=(1/3)*pi*r1^2*h1
we know that 8/18=4/9=r1/h1
4h1/9=r1
Cancel the pi, and multiply by 3 to clear the 1/3
288=r1^2*h1=(4h1/9)^2*h1=(16h1^2/81)*h1
h1^3=288*81/16=23328/16
h1=1458^(1/3)=11.34 inches.

Answer by ikleyn(52803) (Show Source):
You can put this solution on YOUR website!
.
The solution by @Boreal is correct (is adequate) if the cone is in position (vertex down; bottom up).

If it is in reversed position (bottom down), then the solution must be corrected.