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

Answer:

The volume increased eightfold.

Step-by-step 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 $\dfrac{V'}{V}$

$\dfrac{3360}{420}=8$

Generalization:

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

2l × 2w × 2h - new dimensions

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