Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
A sphere of maximum volume is cut out from a solid hemisphere of radius $r$. The ratio of the volume of the hemisphere to that of the cut out sphere is :
(a)3 : 2
(b)4 : 1
(c)4 : 3
(d)7 : 4
Answer
Answer (as printed): B
Explanation
Volume of hemisphere $=\frac{2}{3} \pi r^{3}$. Volume of biggest sphere = Volume of sphere with diameter $r=\frac{4}{3} \pi\left(\frac{r}{2}\right)^{3}=\frac{1}{6} \pi r^{3}$. ∴ Required ratio $=\frac{\frac{2}{3} \pi r^{3}}{\frac{1}{6} \pi r^{3}}=\frac{4}{1}$ i.e. 4 : 1.
Explanation as extracted from the printed page; notation may be imperfect.