Question

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?

Answer 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.

Answer 2

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