Homework Help: math-need help

Posted by jujube on Monday, January 21, 2008 at 4:49pm.

A right rectangular tank with a 12 unit by 8 unit base is filled with water to a depth of 5 units. The water rises 1.5 units when a solid cube is completely submerged in the tank. In simplest radical form, the edge of the cube is k*cube root of w units. Find the value of k plus w.

math-need help - Damon, Monday, January 21, 2008 at 5:11pm
The volume of the cube raises the water 1.5 units
so the volume of the cube is:
1.5 * 12 * 8 units cubed
so
V = 144 units^3
that is the cube of the edge of the cube
144 = (k* w^1/3)^3 = k^3 w
That is all I can do with the information given.
math-need help - Damon, Monday, January 21, 2008 at 5:18pm
Oh, I see from your earlier questions that you are doing only integer answers
Well, 144 is a handy number being 12^2
so
2 * 2 * 3 * 2 * 2 *3
two will have to be cubed
8 * 18 is 2^3 * 18
So I think k = 2 and w = 18

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