Question

you are packing a boxef gift in the largest shipping box. The dimensions of the shipping box are all 1.5 times the dimensions of the Box gift. The volume of the shipping box 1080 cubic inches. What volume of the shipping box is not taken up by the gift box​

Answer 1

`2.375 {x}^(3) \: cubic \: inches`

Explanation:

Suppose the length of the gift box is x inches.

Then the length of the shipping box would be 1.5x inches.

So now we know that the volumes of the gift box and the shipping box are respectively:

V(gift) = x^3 cubic inches

V(shipping) = (1.5x)^3 = 3.375x^3 cubic inches

The volume in the shipping box that is not taken up by the gift box would then be:

V(remain) = V(shipping) - V(gift) = 3.375x^3 - x^3 = 2.375x^3 cubic inches