Question : How many solid spheres are made if a metallic cone of radius 12 cm and height 24 cm is melted into spheres of radius 2 cm each?
Option 1: 105
Option 2: 101
Option 3: 108
Option 4: 103
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Correct Answer: 108
Solution :
Given: A metallic cone of radius 12 cm and height 24 cm is melted into spheres of radius 2 cm each
We know,
The volume of a cone = $\ \frac {1}{3}\pi r^2h$, where $r$ and $h$ are the radius and height of the cone respectively.
So, the volume of the cone = $\frac{1}{3}×\pi×12^2×24$ cm
3
.
Also the volume of a solid sphere = $\frac{4}{3}\pi R^3$, where $R$ is the radius.
So, the volume of a solid sphere = $\ \frac {4}{3}×\pi×2^3$ cm
3
.
Therefore, the required number of solid spheres
= $\frac{\frac{1}{3}×\pi×12^2×24}{\frac{4}{3}×\pi×2^3}$
= $\frac{144×24}{4×8}$
= $108$
Hence, the correct answer is 108.
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