A rectangular block has faces with the areas of 48, 72, and 96. What is the volume of the block?

Question

A rectangular block has faces with the areas of 48, 72, and 96. What is the volume of the block?

Answer 1

draw out a rectangle, label the sides as a, b, and c.

let ac = 48, bc = 72, ab = 96.

these numbers all look like they're divisible by 12.

pick b = 12, since bc and ab are both big numbers :)

if b=12, using bc=72 --> c=6

if c=6, using ac=48 --> a = 8.

check your answer:

8x6 =48

12x6 =72

8x12=96

so the lengths must be 6,8,12.

v=abc

v=6x8x12=576 sq.units

*edit- formatting

Answer 2

Multiply them.  Length times width times height.