Question

X

If the edges of a rectangular prism are increased by a scale factor of 3, how will the volume change
O A. The new volume is 3 times the old volume,
B. The new volume is 9 more than the old volume.
O C. The new volume is 9 times the old volume,
D. The new volume is 27 more than the old volume,
O E. The new volume is 27 times the old volume,

Answer 1

E. The new volume is 27 times the old volume.

Explanation:

A rectangular prism has dimensions width w, height h and length l. It's volume is given by:

`V = wdl`

Edges of a rectangular prism are increased by a scale factor of 3

Each dimensions is multiplied by 3, and the volume is:

`V_m = 3w(3d)(3l) = 3*3*3wdl = 27wdl`

How will the volume change?

`(V_m)/(V) = (27wdl)/(wdl) = 27`

Thus, the volume is multiplied by 27, that is, it is 27 times the old volume, and the correct answer is given by option E.