A solid metallic ball of radius 9 cm is melted to form cylinders of ra

1.	A solid metallic ball of radius 9 cm is melted to form cylinders of radius 6 mm and height 1 cm. Find the number of such solid cylinders that can be formed.1. 22002. 30003. 25004. 2700
Answer» Correct Answer - Option 4 : 2700 Given: Radius of ball = 9 cm Radius of cylinder = 6 mm = 0.6 cm Height of cylinder = 1 cm Concept: The volume of the spherical ball will be equal to the total volume of all the cylinders that can be formed. Formula used: Volume of sphere = (4/3)πr³ Volume of cylinder = πr²h Calculation: Let, ‘n’ be the number of cylinders that can be formed; ∴ Volume of spherical ball = n × Volume of one cylinder. ⇒ (4/3)πr³ = n × πr²h ⇒ (4/3) × (22/7) × 9 × 9 × 9 = n × (22/7) × 0.6 × 0.6 × 1 ⇒ n = 2700

A solid metallic ball of radius 9 cm is melted to form cylinders of radius 6 mm and height 1 cm. Find the number of such solid cylinders that can be formed.1. 22002. 30003. 25004. 2700

Answer» Correct Answer - Option 4 : 2700

Given:

Radius of ball = 9 cm

Radius of cylinder = 6 mm = 0.6 cm

Height of cylinder = 1 cm

Concept:

The volume of the spherical ball will be equal to the total volume of all the cylinders that can be formed.

Formula used:

Volume of sphere = (4/3)πr³

Volume of cylinder = πr²h

Calculation:

Let, ‘n’ be the number of cylinders that can be formed;

∴ Volume of spherical ball = n × Volume of one cylinder.

⇒ (4/3)πr³ = n × πr²h

⇒ (4/3) × (22/7) × 9 × 9 × 9 = n × (22/7) × 0.6 × 0.6 × 1

⇒ n = 2700

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