Arectangular 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?

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

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

So, the volume of the prism is

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

We have

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