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 − 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

The sphere formula is V = (π/3) x^2 (3R − x) = (π/3) x^2 (45 − x). Evaluate the choices:

- x = 12.25: V ≈ (π/3)(12.25^2)(32.75) ≈ 5,144.6 ft^3
- x = 12.5: V ≈ (π/3)(12.5^2)(32.5) ≈ 5,315.8 ft^3
- x = 12.75: V ≈ 5,488.9 ft^3
- x = 13.25: V ≈ larger

5300 ft^3 lies between the 12.25 and 12.5 values and is closest to 12.5 ft.

Answer: 12.5 ft.