Question #282156

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

the x-axis.


1
Expert's answer
2021-12-23T12:31:01-0500

Curve: x2+y2=9x^{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=43πr3V=\frac{4}{3} \pi r^{3} (volume of sphere)

 V=43π(3)3[ radius =3]=36πVolume =36π\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}



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