Twelve solid spheres of the same size are made by melting a solid meta

1.	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 is1. 4 cm2. 2 cm3. 3 cm4. 6 cm
Answer» 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

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 is1. 4 cm2. 2 cm3. 3 cm4. 6 cm

Answer» 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

Discussion

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