Question : A metallic sphere of radius 21 cm is melted and then recast into smaller cones, each with a 7 cm radius and a height of 3 cm. Find the number of cones obtained.
Option 1: 225
Option 2: 325
Option 3: 522
Option 4: 252
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Correct Answer: 252
Solution :
Let the number of cones made be $n$.
In this case, the metallic sphere is melted and then cast into smaller cones.
So, Volume of Sphere $= n\times$ Volume of cone
⇒ $\frac{4}{3}\pi r{_s}^3=n\times\frac{1}{3}\pi r{_c}^2h$ where $r_s$ is the radius of the sphere, $r_c$ is the radius of the cone, and $h$ is the height of the cone.
⇒ $4\times r{_s}^3=n\times r{_c}^2h$
⇒ $4\times (21)^3=n\times (7)^2\times 3$
⇒ $n=\frac{4\times 21\times 21\times 21}{7\times 7\times 3}$
⇒ $n=4\times3\times 21$
⇒ $n=252$
Hence, the correct answer is 252.
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