SOLUTION: The volume of a cube is 176 less than the volume of a rectangular prism. The height is the same. The length of the prism is 6 more than the cube and the width of the prism is 2 mor
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Question 617979: The volume of a cube is 176 less than the volume of a rectangular prism. The height is the same. The length of the prism is 6 more than the cube and the width of the prism is 2 more than the cube. Find the length of the cube.
This was on my algebra final today and it stumped me... I literally got every single other question wrong but I just couldn't figure this one out. Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! Height of both cube and rectangular prism is same
Let length of cube be x
Length of prism = x+6
width of prism = x+2
The volume of prism - volume of cube = 176
x= h for the prism
(x+6)(x+2)*x -x^3= 176
x(x^2+8x+12)-x^3=176
x^3+8x^2+12x-x^3= 176
8x^2+12x-176=0
/4
2x^2+3x-44 =0
2x^2+11x-8x-44=0
x(2x+11)-4(2x+11)=0
(2x+11)(x-4)=0
x= 4 OR -11/2
Ignore negative value
x=4 side of cube = 4 units
Check
10*6*4=240
4*4*4=64
240-64= 176
