Polynomial Equations and Inequalities

Question

Abdi 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.

Answer 1

If the volume increases by 9 the length dimensions have to increase by ∛9=2.08 approx, but that also increases the height. I suspect that it's the ground area that needs to increase, and the height remains the same. If this is the case then only the length and width have to be increased. This increase is √9=3.

Assuming the height is 2m, then length and width are 4m and 1m. The current volume is 8m³. If the length and width are increased by 3 then they become 12m and 3m, and the total volume is 72m³, which is 9 times 8m³.

If all the dimensions are changed by the same amount, the new dimensions would be 2.08m, 4.16m, 8.32m, resulting in volume 72m³. This would make the height 4.16m which is probably impractical.