Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2010 · Marks: · Difficulty:
The ratio of the volume of a cube to that of a sphere which will fit inside the cube is
(a)$4: \pi$
(b)4 : $3 \pi$
(c)$6: \pi$
(d)$2: \pi$
Answer
Answer (as printed): C
Explanation
Let the edge of the cube be $a$. Then, volume of the cube $=a^{3}$. Radius of the sphere $=(a / 2)$. $$\begin{aligned} & \text { Volume of the sphere }=\frac{4}{3} \pi\left(\frac{a}{2}\right)^{3}=\frac{\pi a^{3}}{6} . \\ & \therefore \text { Required ratio }=a^{3}: \frac{\pi a^{3}}{6}=6: \pi . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.