Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
The volume of the largest possible cube that can be inscribed in a hollow spherical ball of radius $r \mathrm{cm}$ is (Hotel Management, 2009)
(a)$\frac{2}{\sqrt{3}} r^{2}$
(b)$\frac{4}{3} r^{2}$
(c)$\frac{8}{3 \sqrt{3}} r^{3}$
(d)$\frac{1}{3 \sqrt{3}} r^{3}$
Answer
Answer (as printed): C
Explanation
Clearly, the diagonal of the largest possible cube will be equal to the diameter of the sphere. Let the edge of the cube be $a$. $$\sqrt{3} a=2 r \Rightarrow a=\frac{2}{\sqrt{3}} r . \quad \therefore \text { Volume }=a^{3}=\left(\frac{2}{\sqrt{3}} r\right)^{3}=\frac{8}{3 \sqrt{3}} r^{3} .$$
Explanation as extracted from the printed page; notation may be imperfect.