Question

Use differentials to approximate the volume of material needed to make a rubber ball if the radius of the hollow inner core is 2 in., and the thickness of the rubber is ⅛ in.

Answer 1

volume of the sphere is $V=\frac{4}{3}\pi r^3$

$dV=\frac{4}{3}\pi (3r^2)dr$

$=4 \pi r^2dr\\=4\pi (4)^2(0.2)=12.8 \pi$