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

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

RELATED QUESTIONS
How would you find the length of a cube with the same volume as a rectangular prism? The... (answered by ikleyn)

The length of a rectangular prism is twice its width. The height of the prism is five... (answered by nyc_function)

The volume of a rectangular prism is 60 cubic inches. The height is 4 inches. What could... (answered by richard1234)

A rectangular prism has a area of 64m2 The height of the prism is 8m. What is the volume... (answered by Fombitz)

A rectangular prism has a base area of 400 square inches. The volume of the prism is 2 ,... (answered by KMST)

the length, width, and height of a rectangular prism are each cut in half. what is the... (answered by MathLover1)

Two rectangular prisms have the same volume. The area of the base of the blue prism is 2... (answered by Theo)

The volume of a rectangular prism is 630 cm3. What is the volume of this prism, measured... (answered by Theo)

There is a prism that has a volume of720 mm determine the length of the prism (answered by Fombitz)