117k views
20 votes
A triangular prism that has a volume of 24 cubic inches is changed by a scale factor of 5. Find the volume of the dilated cube.

A. 120

B. 600

C. 3000

D. 3600

1 Answer

4 votes

Answer: 3000 (choice C)

==========================================================

Reason:

If the linear scale factor is 5, then the volume scale factor is 5^3 = 125

Meaning we'll multiply the old volume by 125 to get the new volume

new volume = 125*(old volume)

new volume = 125*(24)

new volume = 3000

---------------

A more in-depth look:

Consider a 2 by 2 by 2 block. Its volume is 2*2*2 = 8

Now multiply each dimension by 5, so we now have a 10 by 10 by 10 block. The new larger volume is 10*10*10 = 1000

The volume ratio is 1000/8 = 125, which matches with the value found earlier.

Since we multiplied each piece by 5, and did so three times, we're really multiplying the volume by 5*5*5 = 125.

User Kos Prov
by
5.4k points