# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/11) | Q#2

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;