A box of crackers has a volume of 48 cubic inches. what is the volume of a similar box that is smaller by a scale factor of 2/3

For this case what you need to know is that the original volume of the cookie box is:

V = (w) * (l) * (h)

Where,

w: width

l: long

h: height.

We have then:

V = (w) * (l) * (h) = 48 in ^ 3

The volume of a similar box is:

V = (w * (2/3)) * (l * (2/3)) * (h * (2/3))

We rewrite:

V = ((w) * (l) * (h)) * ((2/3) * (2/3) * (2/3))

V = (w) * (l) * (h) * ((2/3) ^ 3)

V = 48 * ((2/3) ^ 3)

V = 14.22222222 in ^ 3

Answer:

the volume of a similar box that is smaller by a scale factor of 2/3 is:

V = 14.22222222 in ^ 3