Question

A cylindrical tank of radius 10 feet is being filled with wheat at the rate of 3/4 cubic feet per minute. The then depth of the wheat is increasing at the rate of

Options

• 1 Cubic feet/minute

• 0.1 Cubic feet/minute

• 1.1 Cubic feet/minute

• 0.5 Cubic feet/minute

Answer 1

1 Cubic feet/minute

Explanation:

Let 'h' be the height (depth) of the cylindrical tank at any instant

Volume of the cylindrical tank = `pir^2h`

∴ V = `100  pih  (10)^2h`  .....`[because r = 10  ft]`

 V = `100  pih`

Rate of change of volume = `(dv)/(dt)`

`(dv)/(dt) = 10pi  (dv)/(dt)`  ......(1)

The tank is filted at the rate of 314 cubic feet per minute i.e.,

`(dv)/(dt)` = 314

From (1), 314 = `100 pi  (dv)/(dt)`

`(dh)/(dt) = 314/(100pi) = 314/(100 xx 3.14)` = 1

Hence, the depth of the tank changes at 1 cubic feet/minute.