SSC CGL 2023 PYQ — Question 56

The correct answer is Option 4 i.e. $\frac{125\pi}{6\sqrt2}$ cm³.

Let's assume the height of the cone h = radius of the cone r = x

Slant height = 5 cm

Slant height = $\sqrt{h^2+r^2}$

⇒ 5 = $\sqrt{x^2+x^2}$

⇒ 5 = x$\sqrt{2}$

⇒ x = 5/$\sqrt{2}$

Volume of the cone = 1/3 πr²h

⇒ $\frac{1}{3}\pi\times(\frac{5}{\sqrt2})^2\times \frac{5}{\sqrt2}$

⇒ $\frac{125\pi}{6\sqrt2}$ cm³