1.2: Estimate an increase in the radius of a sphere

The volume of a sphere is $\displaystyle 500\,\mathrm{cm}^3$.

(a) Calculate the radius, in $\displaystyle \mathrm{cm}$ to 3 significant figures, of the sphere.

The surface area of the sphere is increased by $\displaystyle 20\,\mathrm{cm}^2$.

(b) Using calculus, find an estimate for the increase in the radius, in $\displaystyle \mathrm{cm}$ to 2 significant figures, of the sphere.