Question

A customer at a self -storage facility was offered a choice between a storage unit shaped like a cube and another unit is 2 feet longer,5 feet shorter than the first unit. The customer thinks that f the volume of the cube is x^3 the volume of the other unit would be x^3-4x^2-11x+30. Is the customer correct ?

Answer 1

Answer:the customer is incorrect

Explanation:

In a cube, all 4 sides are equal. The volume of a cube that has x as the length of each side would be x^3

If the customer thinks that f the volume of the cube is x^3, it means that each side is x. Then the other storage unit offered to the customer is 2 feet longer,5 feet shorter than the first unit. Its dimensions would be (x+ 2) feet, (x - 5) feet and x feet

The volume of the other storage unit should be

x[(x + 2)(x - 5)] = x(x^2 - 5x + 2x + 10)

= x(x^2 - 3x + 10)

= x^3 - 3x^2 + 10x

Answer 2

Answer: No, the Volume is x^3 - 3x^2 - 10x

Explanation:

Since the volume of the cubic storage unit is x^3

Therefore,

Length = x

Width = x

Height = x

For the new storage unit

Length = x + 2

Width = x

Height = x - 5

Volume = ( x + 2)(x)(x -5)

V = x (x^2 -3x - 10)

V = x^3 - 3x^2 - 10x

Therefore, the volume of the new storage unit is x^3 - 3x^2 - 10x