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Be certain to limit yourself to the four permissible calculator functions.

The town of Calcuville has a water tower whose tank is a circular ellipsoid, formed by rotating an ellipse around its minor axis. The tank is 20 feet tall and 50 feet wide.

(a) If there are 7.46 gallons of water per cubic foot, what is the capacity of the tank to the nearest 1000 gallons?

(b) Calcuville imposes water rationing regulations whenever the tank is only one quarter full. How deep is the water in the tank when water rationing becomes necessary?

(c) During peak usage, 5000 gallons of water are used per hour. How fast is the water level dropping if it is 12 feet deep when peak usage begins?

Solution

LEGEND

The four permissible (TI-83) calculator functions that we're allowed to use to solve these wiki questions:

1. Graphing the function: [Y=] [GRAPH]
2. Determining the roots or y-intercepts: [2nd] [CALC] [2:zero]
3. Numerically differentiating a function: [2nd] [6:dy/dx] or [MATH] [8:nDeriv]
4. Numerically integrating a function: [2nd] [7:∫f(x)dx] or [MATH] [9:fnInt]