Question

A dumpster in the shape of a rectangular prism has a volume of 240 cubic feet. The length of the dumpster is 4 feet less than twice the width w, and the height is 1 foot less than the width.
Find the equation, in terms of w, that could be used to find the dimensions of the dumpster in feet.

Answer 1

Answer:

240 = w (2w − 4) (w − 1)

Step-by-step explanation:

Volume of a rectangular prism is width times length times height.

V = wlh

Given:

V = 240

l = 2w − 4

h = w − 1

Substituting:

240 = w (2w − 4) (w − 1)

Answer 2

Answer:

2$w^{3}$-6$w^{2}$+4w=240

Step-by-step explanation:

The length and height are given in terms of the width. Width =w; Length =(2w−4); Height =(w−1); and the Volume is equal to the product of the three. Therefore, we can set up the equation as follows:

w×(2w−4)×(w−1)=240

To finish, we distribute and combine like terms:

(2$w^{2}$−4w)×(w−1)=240

2$w^{3}$−2$w^{2}$−4$w^{2}$+4w=240

2$w^{2}$−6$w^{2}$+4w=240

Therefore, 2$w^{3}$−6$w^{2}$+4w=240 is our equation for the dimensions of the dumpster in terms of w.