The volume, V, of a sphere, is given by the formula \(V = \frac{4}{3}\pi r^3\),

where r is the radius of the sphere.

The rate of change of the volume with respect to the radius is given by the derivative of the volume with respect to the radius, which is:

\(\frac{\mathrm dV}{\mathrm dr} = 4\pi r^2\).

When r = 1, the rate of change of the volume with respect to the radius is \(4\pi (1)^2 = 4\pi\).