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: Option B
Solution(By Examveda Team)
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 :
$$\eqalign{ & = \frac{{\frac{2}{3}\pi {r^3}}}{{\frac{1}{6}\pi {r^3}}} \cr & = \frac{4}{1}i.e.,4:1 \cr} $$
Related Questions on Volume and Surface Area
A. 12$$\pi$$ cm3
B. 15$$\pi$$ cm3
C. 16$$\pi$$ cm3
D. 20$$\pi$$ cm3
In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
A. 75 cu. m
B. 750 cu. m
C. 7500 cu. m
D. 75000 cu. m
A. 84 meters
B. 90 meters
C. 168 meters
D. 336 meters
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