If the sum of slant height, height and radius is (9 + 3√3) cm, then what is the volume of the cone (with vertex angle 120°)?

Half vertex angle = 60°. So r = l sin 60° = l√3/2, h = l cos 60° = l/2. Sum: l + l/2 + l√3/2 = l(3 + √3)/2 = 9 + 3√3 = 3(3 + √3). So l = 6. Then r = 3√3, h = 3. Volume = (1/3)πr²h = (1/3)π(27)(3) = 27π. Hmm, that gives (a). Let me recheck: r² = 27, so V = (1/3)π(27)(3) = 27π cubic cm. Actually 27π is option (a). Wait, r = l sin 60° = 6 × √3/2 = 3√3. r² = 27. h = 3. V = (1/3)(π)(27)(3) = 27π. Answer (a) 27π.