Question

The volume of a spherical balloon is increasing at a constant rate of 50 cm3 per second. Find the rate of increase of the radius when the radius is 10 cm. [Volume of a sphere ]

Solution

     i.
 

We are given that;

We are required to find rate of change of radius;

Therefore;

For rate of change of radius;

We have  so we need to find .

Expression for the volume of the sphere is;

                                       

Therefore;

Rate of change of  with respect to  is derivative of  with respect to  ;

Therefore, rate of change of volume of sphere is;

Rule for differentiation of  is:

Rate of change  of  with respect to  at a particular point  can be found by substituting x-coordinates of that point in the expression for rate of change;

Hence rate of change of volume when .

Finally;