Pamela wants to buy a suitcase whose dimensions are 1 1/2 times those of her 28 times 16 times 8 inch suitcase. How is the ratio of the volumes related to the ratio of corresponding dimensions? What is the ratio of the volumes?

Multiply the dimensions by 1.5 and Pamela's suitcase becomes 42" x 24" x 12".

Volume of 28" x 16" x 8": 3584 in^3

Volume of 42" x 24" x 12": 12,096 in^3

The volume ratio is 3.375, and yes, you have to cube it.

ok

volume=length times width times height

her current suitcase volume is 28*16*8=3584 cubic inches

her new one will have each dimention mulipled by 1 and 1/2 or 1.5

so

newV = (1.5*28) * (1.5*16) * (1.5*8)

newV=12096 cubic inches

ratio is 12096/3584=3.375=1.5*1.5*1.5

the ratio is new:old=3.375:1