$\"\"$

(a).

(i) Find the rate of change in volume of the sphere $\"\"$ when $\"\"$ .

The rate of change of radius is $\"\"$ .

The volume of the sphere $\"\"$ .

Apply derivative on each side with respect to $\"\"$ .

$\"\"$

Power rule of the deivative : $\"\"$ .

$\"\"$ .

Substitute $\"\"$ and $\"\"$ in the above equation.

$\"\"$

$\"\"$ .

(ii)

Find the rate of change in volume $\"\"$ when $\"\"$ .

$\"\"$

Substitute $\"\"$ and $\"\"$ in the above equation.

$\"\"$

$\"\"$ .

$\"\"$

(b).

Rate of change in volume is $\"\"$ .

Rate of change of the volume of the sphere depends on the values of the rate of change in radius and radius of the sphere.

The rate of change of volume of the sphere is not constant even when the rate of change of radius is constant beacause it depends on the value of radius.

$\"\"$

(a) $\"\"$ and $\"\"$ .

(b) The rate of change of volume of the sphere is not constant even when the rate of change of radius is constant beacause it depends on the value of radius.