Applications of Differentiation: Exercise 3

Introduction
Exercise 3 will focus on rates of change.

1.  A metal cube is expanding so that its sides change at the rate of 2cm/s. Find the rate of change of its surface area when its volume is 125 cm³.
2. The radius of a circle is increasing at the constant rate of 0.5m/s . Find the increasing rate of the surface area of the circle when the perimeter is 12 m.
3. An inverted right circular cone has a base radius of 3 m and a height of 9 m. The cone is full of water. If water is leaking from the bottom at the rate of 2m³/min , find the rate of fall of the water level when the water level is 6 m high.
4. A hemispherical bowl of radius 8 m contains water which is flowing into it at a constant rate. When the height of the water is h cm, the volume V cm³ of the water in the bowl is given by
   
   
   Find the rate at which the water level is rising when h = 5cm, given that the time taken to fill the bowl is 2 minutes.