Find the rate of change of the volume of a sphere with respect to its

1.	Find the rate of change of the volume of a sphere with respect to its diameter.
Answer» The volume of a Sphere \(=\frac{1}{6}\pi D^3\) Where D = diameter of the Sphere We need to find, \(\frac{dV}{dD}\) where V = Volume of the sphere and D = Diameter of the Sphere. \(\frac{dV}{dD}=\frac{\pi D^2}{2}\) Hence, Rate of change of Volume of Sphere with respect to the diameter of the Sphere is given by \(\frac{\pi D^2}{2}.\)

Find the rate of change of the volume of a sphere with respect to its diameter.

Answer»

The volume of a Sphere \(=\frac{1}{6}\pi D^3\)

Where D = diameter of the Sphere

We need to find, \(\frac{dV}{dD}\) where V = Volume of the sphere and D = Diameter of the Sphere.

\(\frac{dV}{dD}=\frac{\pi D^2}{2}\)

Hence, Rate of change of Volume of Sphere with respect to the diameter of the Sphere is given by \(\frac{\pi D^2}{2}.\)