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
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #32165)