The height of a cone is equal to its base radius and its volume is $$72 \pi cm^3$$. What is its curved surface area in $$cm^2$$ ?

Given, 

Height of Cone = Radius of same cone

Volume of cone = 72 $$\pi\ cm^3$$

As we know,

Volume of cone = $$\frac{1}{3}\pi r^2h\ $$

Now, 

$$\longrightarrow\ \frac{1}{3}\pi r^2r\ $$ (Given, h = r)

$$\longrightarrow\ \frac{1}{3}\pi r^3=72\pi\ $$

$$\longrightarrow\ r^3=216$$

$$\longrightarrow\ r=6cm$$,  h = 6 cm

$$\longrightarrow\ l^2=h^2+r^2$$

$$\longrightarrow\ l^2=36+36$$

$$\longrightarrow\ l=6\sqrt{\ 2}cm$$

Curved Surface area of Cone : $$\pi\ rl$$

= $$\pi\ 6\times\ 6\sqrt{\ 2}$$

= $$36\sqrt{\ 2}$$

Hence, Option B is correct.