Answer to Question #282156 in Calculus for james

Question

Find the volume generated by revolving the area enclosed by the curve x2 + y2 = 9 about

the x-axis.

Answer 1

Curve: $x^{2}+y^{2}=9$

It is an equation of the circle, with radius 3 and centered at the origin.

If you notate a circle about x-axis,

Yow will get a sphere of the same radius and also centered at the origin.

so, volume: $V=\frac{4}{3} \pi r^{3}$ (volume of sphere)

 $\begin{aligned} \Rightarrow V &=\frac{4}{3} \pi(3)^{3} \quad[\because \text { radius }=3] \\ &=36 \pi \\ \therefore \quad \text {Volume } &=36 \pi \end{aligned}$