Question : The radius of a solid sphere is 42 cm. It is melted to form identical small solid spheres whose radius is 7 cm. What is the number of small solid spheres obtained?
Option 1: 64
Option 2: 36
Option 3: 216
Option 4: 125
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Correct Answer: 216
Solution :
Given: The radius of a solid sphere is 42 cm.
It is melted to form identical small solid spheres whose radius is 7 cm.
The volume of the sphere of radius $r$ is $\frac{4}{3}\pi r^3$.
Let $x$ be the maximum number of spheres that can form.
The volume of the sphere $=\frac{4}{3}\times\pi \times(42)^3$
It melts and forms a small sphere.
The sphere's volume = The small sphere's volume
⇒ $\frac{4}{3}\times\pi \times(42)^3=x\times\frac{4}{3}\times\pi \times(7)^3$
⇒ $x=6\times 6\times 6=216$
Hence, the correct answer is 216.
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