The dimensions of a box are 20" by 30" by 4". The volume of the box is 2400 inches cubed. If each dimension is doubled the new volume would be the original volume times the: a)scale factor b)scale factor squared c)scale factor cubed

old volume = (l)(w)(h)

new volume = (2l)(2w)(2h) = 2^3(lwh)

mmmhhh?

Thanks, I appreciate it.

To find the new volume after doubling each dimension, we'll need to calculate the scale factor first.

The scale factor is the ratio of the new dimension to the original dimension. Since we are doubling each dimension, the new dimensions would be 40" by 60" by 8".

The scale factor for each side can be found by dividing the new dimension by the original dimension:

S1 = 40" / 20" = 2
S2 = 60" / 30" = 2
S3 = 8" / 4" = 2

Now, let's calculate the new volume by multiplying the dimensions together:

New Volume = (40" x 60" x 8") = 19200 inches cubed

To compare the new volume with the original volume, we can divide the new volume by the original volume:

New Volume / Original Volume = 19200 inches cubed / 2400 inches cubed = 8

The answer is (c) scale factor cubed. When each dimension is doubled, the new volume is the original volume times the scale factor cubed.