$x-$axis to create $3$D shapes. Consider the equation $f(x)=\sqrt[\phantom{2}]{25-x^2}$ and its graph.

A$.$ Revolve the function about the $x-$axis to draw a sphere.

B$.$ Revolved around the $x-$axis it would produce a sphere with radius $5.$ What is the volume of that sphere?

C$.$ Solve the definite integral ${\displaystyle \underset{-5}{\overset{5}{}}}(f(x){)}^{2}dx={\displaystyle \underset{-5}{\overset{5}{}}}(\sqrt[\phantom{2}]{25-x^2}{)}^{2}dx$ to calculate the volume.