Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is
1. 4 cm
2. 2 cm
3. 3 cm
4. 6 cm
1. 4 cm
2. 2 cm
3. 3 cm
4. 6 cm
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Correct Answer – Option 2 : 2 cm
Given
Diameter of base of cylinder = 2 cm
Height of cylinder = 16 cm
Formula used
Volume of sphere = (4/3)πr3, where r is the radius of the sphere
Volume of Cylinder = πR2h, where R is the radius of circular base and h is the height of cylinder
Calculation
Radius of base of cylinder = 1 cm
Volume of cylinder = πR2h
⇒ π(1)2(16) = 16π
Volume of 12 spheres = 12 × (4/3)πr3
⇒ 16πr3
Volume of cylinder = volume of 12 spheres
⇒ 16π = 16πr3
⇒ r3 = 1
⇒ r = 1 cm
∴ Diameter = 2 × radius = 2 × 1 = 2 cm