Hi Sanju09,
Is Answer D ?

Regards,
Uva

The maximum radius is R = 4.8 (see diagram).

The curved surface area of a cone is pi * R * L where L = slant height.

We have 2 cones:

So total surface area = pi * R * (L1 + L2)
= 3.14 * 4.8 * (6 + 8) = 211 (approx.)

Answer = (D)

Please draw on your own according to the following explanation:

∆ABC has AB = 6, BC = 10, and CA = 8, and consequently it is right angled at A. Mathsbuddy did justice to the situation that I described in the question. Now drop perpendicular from A on BC to meet BC in D. This AD would serve as the common radius in the resulting solid so generated. Area of ∆ABC is ½ AB.AC = ½ BC.AD = 24, hence AD = 4.8; for approximation purposes we'll later on take AD = 5.

The curved surface area of a cone = π (Base Radius) (Slant Height)

[Let's take π = 3 only]

The collective curved surface area of the solid so generated would equal

π(5)(6) + π(5)(8) = [spoiler]90 + 120 = 210. It's D.[/spoiler]