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 :
Options:
A . 3 : 2
B . 4 : 1
C . 4 : 3
D . 7 : 4
Answer: Option B Volume of hemisphere = $$\frac{2}{3}\pi {r^3}$$ Volume of biggest sphere : = Volume of sphere with diameter r $$\eqalign{ & = \frac{4}{3}\pi {\left( {\frac{r}{2}} \right)^3} \cr & = \frac{1}{6}\pi {r^3} \cr} $$ ∴ Required ratio : $$\eqalign{ & = \frac{{\frac{2}{3}\pi {r^3}}}{{\frac{1}{6}\pi {r^3}}} \cr & = \frac{4}{1}i.e.,4:1 \cr} $$
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