Question

The graph shown represents the volume of petroleum in a spherical tank with a 15-foot radius as a function of the height of the liquid, in feet. This relationship can be modeled by the equation y = 15πx2 −1/3 πx3. What is the approximate height of the petroleum in the tank when the volume is 5,300 ft3?

12.25 ft
12.5 ft
12.75 ft
13.25 ft

Answer 1

We solve π(15x^2 − (1/3)x^3) = 5300 → 15x^2 − (1/3)x^3 = 5300/π ≈ 1687.0.

Evaluate the volume at the choices:
- x = 12.25 → V ≈ π(1638.18) ≈ 5146 ft^3 (too low)
- x = 12.5 → V ≈ π(1692.708) ≈ 5318 ft^3 (slightly high)

Interpolating gives x ≈ 12.47 ft, so the closest choice is 12.5 ft.