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
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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