Question

A cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic metre per hour. Then at which rate the depth of the wheat is increasing.

Answer 1

Given: A cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic metre per hour.

To find: At which rate the depth of the wheat is increasing?

Solution:

• Lets consider the radius as r, volume as V and the depth as h of the tank.

• We have given that cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic metre per hour, so:

                 dV /dt = 314 m³ / hr

• Now volume of cylinder is: πr²h

                V = πr²h

                differentiating both sides w.r.t time, we get:

                dV /dt = d( πr²h)/dt

                314 = d( π x 10² x h)/dt

                314 = d( 100πh)/dt

• As 100π is common, so:

                100π x d(h)/dt = 314

                d(h)/dt = 314 / 100π

                d(h)/dt = 314 / 100 x 3.14

                d(h)/dt = 314 / 314

                d(h)/dt = 1

Answer:

           So, at 1 m / hr  rate the depth of the wheat is increasing.