If a2 + b2 + c2 = 1, what is the maximum value of abc ?

Answer: Option B

a² + b² + c² = 1
So, the maximum value of a² b² c² = $$\frac{1}{3}$$ × $$\frac{1}{3}$$ × $$\frac{1}{3}$$ = $$\frac{1}{27}$$
(∵ when sum of three positive quantities is fixed, the product will be maximum when the quantities are equal)
Hence, maximum value of abc = $$\frac{1}{\sqrt{27}}=\frac{1}{3\sqrt{3}}$$