Question

Find the volume of the solid obtained by rotating the region enclosed by  𝑥=√6sin(𝑦)

 and 𝑥=0

 about the 𝑦-

axis over the interval 0≤𝑦≤𝜋.

Answer 1

Volume can be calculated by the formula:

$V=\pi\int_0^\pi(\sqrt{6\sin{y}})^2dy=\pi\int_0^\pi6\sin{y}dy=$$-6\pi\cos{y}|_0^\pi=-6\pi(-1-1)=12\pi$

Answer: $V=12\pi$ .