Question

Bob has designed a rectangular storage unit to hold large factory equipment. His scale model has dimensions 1 m by 2 m by 4 m. By what amount should he increase each dimension to produce an actual storage unit that is 9 times the volume of his scale model?

Answer 1

volumes of similar solids are proportional to the cube of their sides
so volume of original = 8m^3
volume of new is 72 m^3

so let's take the smallest dimension of 1 m , since it is a unit dimension.

8/72 = 1^3/x^3
8x^3 = 72
x^3 = 9^(1/3)
x = 9^(1/3) = appr 2.08

So, he should increase each dimenstion by a factor of 2.08
or
the new dimensions should be 2.08 by 4.16 by 8.32 m
check:
(2.08(4.16)(8.32) = 71.99 , not bad using 2 decimal accuracy