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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