Question

The volume of a figure is x^3-9x. The surface area of another figure is 8x^2. disregarding the units, the volume of the first figure equals the surface area of the second figure. What are the possible values of x? explain your reasoning in 1 short sentence.

Answer 1

Solve x^3 - 9x = 8x^2 ⇒ x^3 - 8x^2 - 9x = 0 ⇒ x(x^2 - 8x - 9) = 0, so x = 0, 9, or −1 (discard −1 if x must be a nonnegative length).