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?

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

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.