A) \[\frac{1}{4}cm\]
B) \[\frac{1}{3}cm\]
C) \[\frac{1}{2}cm\]
D) 1 cm
Correct Answer: D
Solution :
Given that the radii of three solid glass balls is 'r' cm, 6 cm and 8 cm, sum of the volumes of the three glass balls \[=\frac{4}{3}\pi {{r}^{3}}+\frac{4}{3}\pi {{(6)}^{3}}+\frac{4}{3}\pi {{(8)}^{3}}\] \[=\frac{4}{3}\pi ({{r}^{3}}+{{6}^{3}}+{{8}^{3}})c{{m}^{3}}\] The volume of the solid sphere of radius 9cm \[\Rightarrow \]\[=\frac{4}{3}\pi {{(9)}^{3}}=243\times 4\pi \] \[\therefore \]\[243\times 4\pi =\frac{4}{3}\pi ({{r}^{3}}+728)\]\[\Rightarrow \]\[r=1\]
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