(Take \[\pi =\frac{22}{7}\] unless otherwise mentioned) A hemisphere of radius 6 cm is cast into a right circular cone of height 75 cm. The radius of the base of the cone is
A) 2.4 cm
B) 2.8 cm
C) 3.5 cm
D) 3.8 cm
Correct Answer: A
Solution :
[a] Let \[{{r}_{1}}\] be the radius of hemisphere and \[{{r}_{2}}\] be the radius of the cone. sGiven that volume of hemisphere = volume cone. \[\frac{2}{3}\pi {{r}_{1}}^{3}=\frac{1}{3}\pi {{r}_{2}}^{2}h\Rightarrow \frac{2}{3}\pi {{6}^{3}}=\frac{1}{3}\pi {{r}^{2}}_{2}\times 75\] \[\Rightarrow {{r}_{2}}^{2}=\frac{2\times 6\times 6\times 6}{75}=\frac{12}{5}=2.4\,\,cm\]
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