Question

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

Answer 1

We know, Volume of rectangular prism = l * b * h
If all dimensions are doubled, then it would be: 2 * 2 * 2 * v
V' = 8V

In Short, Volume will increase to it's 8 times

Hope this helps!

Answer 2

Answer: The volume will become 8 times.

Step-by-step explanation:  Given that a rectangular prism has base of dimensions 5 cm by 7 cm and height of the prism is 12 cm.

We are to find the change in volume if all the dimensions are doubled.

The VOLUME of a rectangular prism having base of dimensions 'l' by 'w' and height 'h' is given by

$V=l\times w\times h.$

Here, l = 7 cm, w = 5 cm and h = 12 cm

So, the volume of the prism is

$V=5\times 7\times 12=420~\textup{cm}^3.$

Now, when all the dimensions are doubled, then we have

l' = 2l = 2 × 5 = 10 cm,

w' = 2w = 2 × 7 = 14 cm,

h' = 2h = 2 × 12 = 24 cm.

The volume f the new prism will be

$V_n=10\times 14\times 24=3360~\textup{cm}^3$

We have

$\dfrac{V'}{V}=\dfrac{3360}{420}=8\\\\\Rightarrow V'=8V.$

Thus, the volume will become 8 times the volume of the original prism.