A) \[6.4\,cm\]
B) \[4.2\,cm\]
C) \[2.1\text{ }cm\]
D) \[5.6\text{ }cm\]
Correct Answer: B
Solution :
Volume of cone of \[r=2.1\text{ }cm\]& \[h=4.1\,cm=\frac{1}{3}\times \pi {{(2.1)}^{2}}(4.1)=\frac{18.08}{3}\pi \,c{{m}^{2}}\] Volume of cone of \[r=2.1\text{ }cm\]& \[h=4.30\text{ }cm\] \[=\frac{1}{3}\times \pi {{(2.1)}^{2}}(4.3)=\frac{18.963}{3}\pi \,c{{m}^{2}}\] Let radius of the sphere be r cm. Now, Volume of sphere = Sum of Volume of both cones. \[\Rightarrow \] \[\frac{4}{3}\pi {{r}^{3}}=\frac{18.081}{3}\pi +\frac{18.963}{3}\pi \] \[\Rightarrow \]\[\frac{4}{3}\pi {{r}^{3}}=\frac{37.044}{3}\pi \,\Rightarrow {{r}^{3}}=\frac{37.044}{4}\] \[\Rightarrow \] \[{{r}^{3}}=9.261\Rightarrow r=\sqrt[3]{9.261}\,\,\,\,\Rightarrow \,\,r=2.1\,cm\] Diameter of sphere \[=4.2\text{ }cm.\]
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