Find the volume of the indicated region.
-the region bounded below by the $x y$-plane, laterally by the cylinder $r = 4 \cos \theta$, and above by the plane $z = 3$
A) $12 \pi$
B) $3 \pi$
C) $36 \pi$
D) $9 \pi$

Question

Quizplus · Accepted Answer

The volume of the region is given by the integral$$V = \int_0^{2\pi} \int_0^4 \int_0^3 r \ dz \ dr \ d	heta = \int_0^{2\pi} \int_0^4 3r \ dr \ d	heta = \int_0^{2\pi} \left[ \frac{3r^2}{2} ight]_0^4 d	heta = \int_0^{2\pi} 24 \ d	heta = 48\pi$$

Find the Volume of the Indicated Region xyx yxy -Plane, Laterally by the Cylinder

Find the Volume of the Indicated Region $x y$ -Plane, Laterally by the Cylinder