Question : The number of solid spheres, each of diameter 6 cm, that could be moulded to form a solid metal cylinder of height 90 cm and diameter 4 cm is:
Option 1: 10
Option 2: 14
Option 3: 16
Option 4: 13
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Correct Answer: 10
Solution : We have, The radius of the sphere, $R$ = 3 cm The radius of the cylinder, $r$ = 2 cm The height of the cylinder, $h$ = 90 cm Now, the required number of solid spheres = $\frac{\text{ Volume of the cylinder}}{\text{Volume of the Sphere}}$ = $\frac{\pi r^2h}{\frac{4}{3}\pi R^3}$ = $\frac{3\times2\times2\times90}{4\times 3\times 3\times 3}$ = 10 Hence, the correct answer is 10.
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