Question

Hans pours the contents of a flour bag out on the floor at a constant speed of 3 cmˆ3/s. On the floor, the flour forms a straight cone with the tip up so the height h is always doubble the radius r. How fast does the radius change at the time the height of the flour-cone is 10 cm?

The correct answer is 0.019 cm/s.

(Implicit derivation)

Answer 1

Volume of a cone of radius r and height h is given by

Now height(h) is always double the radius, i.e.,

As the flour bag is poured the volume of the cone formed increases with time.

Rate of change of volume of the cone is

Now flour is being poured at the rate of

Also

Height=10 cm

Hence radius=height/2=5 cm

This is the rate of change of radius.