Question : A thousand solid metallic spheres of 6 cm diameter each are melted and recast into a new solid sphere. The diameter of the new sphere (in cm) is:
Option 1: 30
Option 2: 90
Option 3: 45
Option 4: 60
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Correct Answer: 60
Solution :
Given: Diameter = 6 cm
Radius = 3 cm
The volume of the sphere = $\frac{4}{3} \pi R^3$ ($R$ is the radius of a new sphere formed)
According to the question,
$1000\times \frac{4}{3}\times \pi \times (\frac{6}{2})^3=\frac{4}{3}\times \pi \times R^3$
$⇒1000\times 3^3=R^3$
$⇒R = 30$ cm
So, the diameter of the new sphere is 2 × 30 = 60 cm.
Hence, the correct answer is 60.
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