If the radius of a sphere is 16 cm and is melted and recast into a sphere of radius 4 cm. Then find the number of small spheres that are cast.
1. 16
2. 32
3. 48
4. 64
1. 16
2. 32
3. 48
4. 64
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Correct Answer – Option 4 : 64
Given:
Radius of an original sphere = 16 cm
Radius of a recast sphere = 4 cm
Formula Used:
Volume of a sphere = (4/3)πr3
Number of recast spheres = Volume of the original sphere/Volume of the recast sphere
Calculation:
Volume of a original sphere = 4/3 π (16)3
Volume of the recast sphere = 4/3 π (4)3
Hence, number of recast spheres = Volume of the original sphere/Volume of the recast sphere
⇒ [(4/3) π (16)3]/[(4/3) π (4)3] = 64
∴ The number of recast spheres is 64.