If there is an error of 0.1% in the measurement of the radius of a sphere, find approximately the percentage error in the calculation of the volume of the sphere.

The pressure p and the volume V of a gas are connected by the relation, , where k is a constant. Find the percentage increase in the pressure, corresponding to a diminution of 0.5% in the volume.

The radius of a sphere shrinks from 10 cm to 9.8 cm. Find approximately the decrease in (i) volume, and (ii) surface area.

Show that the relative error in the volume of a sphere, due to an error in measuring the diameter, is three times the relative error in the diameter.

Verify Rolle’s theorem for each of the following functions: