find volume when rotating about the x-axis and y-axis

Question

Suppose that R is the finite region bounded by f(x)=√x and g(x)=x/3.

Find the exact value of the volume of the object we obtain when rotating R about the x-axis.

V=

Find the exact value of the volume of the object we obtain when rotating R about the y-axis.

V=

Answer 1

This Desmos graph provides all the details:

desmos.com/calculator/bbvkssjpfv