The height and width of a rectangular prism are each 2 inches shorter than the length of the prism. The volume of the prism is 40 cubic inches. Approximate the dimensions of the prism to the nearest hundredth.

Question

anonymous · Answer

h = L - 2
w = L - 2
volume = L*w*h, or
40 = L * (L-2) * (L-2)

anonymous · Answer

I got to 40 = x^3 - 4x^2 + 4x. what i have to do next ?

alekos · Answer

we have to solve a cubic polynomial to get a value for x

x^3 - 4x^2 +4x -40 = 0

alekos · Answer

By hand I worked out that the root had to be somewhere between 4 and 5, but  
i had to use a cubic equation calculator for this otherwise it's too cumbersome.

x = 4.8669    or x  = 4.87 to the nearest hundredth

i'll let you work out the dimensions