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

Question

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

lethu · Answer

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.

Answer: 3000 (choice C)

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