Question

Marianne and faith are upgrading the storage shed in their backyard. the existing shed has the shape of a rectangular prism with dimensions 1 m by 2 m by 4 m. By what amount should they increase each dimension so that the new shed is 9 times the volume of the original shed? Provide a full algebraic solution.
volume grows as the scale cubed, so multiply each dimension by ∛9
To see this, suppose each dimension is multiplied by k. Then you want
(kx)(ky)(kz) = 9xyz
k^3 xyz = 9xyz
k^3 = 9
Good luck getting the right tape measure!

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