The vertical angle of right circular cone is 2 and the slant height is radic 2 r cm What is the volu...........

Quantitative Aptitude (CDS) Mensuration 3D

The vertical angle of right circular cone is $\pi$ /2 and the slant height is √2 r cm. What is the volume of the cone in cubic cm?

$\pi$ r³

9 $\pi$ r³

$\pi$ r³ / 3

D. 3 $\pi$ r³

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Explanation:

Let the radius of base circle of cone be r cm
Given that slant height(l) = √2r cm
Then, height of cone (h) = $\sqrt{l^{2}-r^{2}}=\sqrt{(\sqrt{2r})^{2} -r^{2} }=\sqrt{r^{2}}=r$
$Hence\: volume\: of\: cone\: =\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi r^{2}r=\frac{\pi r^{3}}{3}$