Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.
-$$y = - 4 x + 8 , y = 4 x , x = 0$$
A) $8 \pi$
B) $96 \pi$
C) $16 \pi$
D) $32 \pi$

Question

Quizplus · Accepted Answer

The region is bounded by the lines $y = -4x + 8$, $y = 4x$, and $x = 0$. The intersection points of the lines are at $x = 1$ and $x = 0$. The volume of the solid is calculated using the disk method: $\int_{0}^{1} \pi ((-4x + 8)^2 - (4x)^2) \, dx$. Solving this integral gives $32\pi$.

Find the Volume of the Solid Generated by Revolving the Region