Question

A rectangular prism has a base that is 5cm by 7cm and a height of 12cm if all dimensions are doubled what happens to the volume?

Answer 1

The volume increased eightfold.

Explanation:

The formula of a volume of a rectangular prism:

`V=lwh`

l - length

w - width

h - height

We have l = 5cm, w = 7cm and h = 12cm.

Substitute:

`V=(5)(7)(12)=420\ cm^3`

Doubled the dimensions:

l' = (2)(5cm) = 10cm, w' = (2)(7cm) = 14cm, h = (2)(12cm) = 24cm.

Calculate the new volume:

`V'=(10)(14)(24)=3360cm^3`

Calculate the quotient
`(V')/(V)`

`(3360)/(420)=8`

Generalization:

V = lwh - the volume of a prism l × w × h

2l × 2w × 2h - new dimensions

V' = (2l)(2w)(2h) = 8lwh = 8V - new volume