Find the total surface area of solid cone of radius 2\(\sqrt{3}\)cm and slanting side 4\(\sqrt{3}\)

A.

8\(\sqrt{3}\pi \)cm2

B.

24\(\pi \)cm2

C.

15\(\sqrt{3}\pi \)cm2

D.

36\(\pi \)cm2

Correct answer is D

Total surface area of a solid cone

r = 2\(\sqrt{3}\)

= \(\pi r^2\) + \(\pi\)rH

H = 4\(\sqrt{3}\), \(\pi\)r(r + H)

∴ Area = \(\pi\)2\(\sqrt{3}\) [2\(\sqrt{3}\) + 4\(\sqrt{3}\)]

= \(\pi\)2\(\sqrt{3}\)(6\(\sqrt{3}\))

= 12\(\pi\) x 3

= 36\(\pi \)cm2