Question

The shortest edge of a rectangular prism is 3 inches, and its volume is 144 cubic inches. A similar rectangular prism has its shores edge equal to 4 inches. What is the approximate volume of the second prism?

Answer 1

The volume of similar 3-D solids is proportional to the cube of their corresponding sides, so

V/144 = 4^3/3^3
V = 144(64/27) = appr 341.33 in^3

or
original: 144 = 3lh
lh = 144/3

new: increased by a factor of 4/3
width = 4
length = (4/3)l
height = (4/3)h
new volume = 4(4/3l)(4/3h)
=(64/9)lh
= (64/9)(144/3) = 341.33

Answer 2

1.09375