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

To find the dimensions of the dumpster given its volume and relationships between dimensions, we express the length and height in terms of the width and substitute these into the volume equation to get 240 = (2W - 4)(W)(W - 1).

Step-by-step explanation:

The student has been given a problem involving the volume of a rectangular prism, representative of a dumpster, which mathematically belongs to the subject of geometry. The volume is given as 240 cubic feet, and the relationships between the dimensions (length, width, and height) are provided. The length L is described as 4 feet less than twice the width W, and the height H is 1 foot less than the width (W). We can express this information in terms of equations:

L = 2W - 4

H = W - 1

The volume V of a rectangular prism is found using the formula V = LWH. Substituting the given expressions in terms of W into the volume equation, we get:

V = (2W - 4)(W)(W - 1)

Since the volume is given as 240 cubic feet, we can write the equation as:

240 = (2W - 4)(W)(W - 1)

This is the equation in terms of the width W that could be used to find the dimensions of the dumpster.

Answer 2

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.