How is the ratio of the volumes related to the ratio of corresponding dimensions and what is the ratio of the volumes

Question

Pamala wants to buy a new suit case whose dimensions are 1 1\2 times those of her 28 x 16 x 8 inch suit case

Answer 1

28x16x8 = 3584

28x1.5 = 42

16x1.5 = 24

8x1.5 = 12

42(24)(12) = 12096

12096/3584 = 3.375 .in^3 times larger volume

If it were a cube, 1 x 1 x 1 = 1 in^3

and dimensions were multiplied by 1 1/2 then the new dimensions would be 1 1/2 by 1 1/2 by 1 1/2 = (1.5)^3 = 3.375 times larger volume

5

If the box is skewed more, such as 1 = 8 x 1/4 x 1/2 then initial volume = 1

and scaled up volume = 8(1.5)(.25)(1.5)(.5)(1.5) = (3.375)

no matter what the scale factor whether 1 1/2 or 2 1/2 or 4 the new volume is increased by a factor of that scale factor cubed. 1.5^3 = 2.25 2.5^3 = 15.625. 4^3 = 64