# Prototype Calculus Question

Find the volume of the solid obtained by rotating the area enclosed by ${\displaystyle y=5-x}$ and ${\displaystyle y=25-x^{2}}$
around the x-axis.

Foundations
Choose either shell or washer method.
Since our rectangles will be trapped between the two functions, and will be rotated around the x-axis (where ${\displaystyle y=0}$,) we find
the inner radius is ${\displaystyle r=5-x}$, represented by the blue line, while
the outer radius is ${\displaystyle R=25-x^{2}}$, represented by the red line.