Question

If the length, width, and height of a rectangular prism is multiplied by 5 will it be *5, *15, *25, *125

Answer 1

How will the volume change? **

Answer 2

Do you know how to find the volume of a prism?

Answer 3

Yes

Answer 4

.... sorry... do you know the formula for the volume of a prism?

Answer 5

yep

Answer 6

Volume = ???? what's the formula?

Answer 7

L*W*H is formula.

Answer 8

ok... so Volume = L * W * H

now since each dimension is multiplied by 5, we have

Volume = (5*L) * (5*W) * (5*H)

can you simplify that form me?

Answer 9

So it's 5 times greater?

Answer 10

no.... how did you get that?

Answer 11

5*L 5*W 5*H

It doesn't give us l,w, and h in the question.

Answer 12

but if you simplify it you'll see how the volume changed.....

Answer 13

It doesn't give us L,W, and H.

Answer 14

yes... L, W, H can be any number, but that's ok...

simplify: New Volume = 5L*5W*5H

Answer 15

multiply the numbers....

Answer 16

25 times greater. Thank you. :D

Answer 17

New Volume = 5L*5W*5H = 5*5*5*L*W*H = 125 * L*W*H = 125 * (original volume)

Answer 18

.. 62^3 original 1550^3 new
62 * 25 = 1550

Answer 19

125 not 25...

Answer 20

Well that's what I got so yeah.

Answer 21

ok...

Answer 22

@AyeItsEmily The original rectangular prism will be similar to the one formed by multiplying the original prism's l, w, and h by 5.

Recall the theorem:
The ratio of volumes of two similar figures is the cube of the scale factor.
The scale factor from the original solid to the enlarged similar one is 1 to 5 or 1/5.
So, (1/5) ^ 3 = ratio of volumes
1/125 is the ratio of the volumes.
So, the volume of the original rectangular prism is multiplied by a factor of 125 to get the volume of the enlarged prism.