Question

How many spherical balls of radius 5 cm can be made from an iron ball of radius 10 cm?

Answer 1

Given :

• Radius of a spherical ball = 5 cm
• Radius of an iron ball = 10 cm

To find :

• Number of spherical balls that can be made from the iron ball

Knowledge required :-

→ Formula of volume of sphere :-

Volume of sphere = 4/3πr³

where,

• Take π = 22/7
• r = radius

Solution :

Volume of the spherical ball :-

⠀⠀⠀⇒ Volume = 4/3πr³

⠀⠀⠀⇒ Volume = 4/3 × π × (5)³

⠀⠀⠀⇒ Volume = 4/3 × π × 125

Volume of the spherical ball = 4/3 × π × 125 cm³

Volume of the iron ball :-

⠀⠀⠀⇒ Volume = 4/3πr³

⠀⠀⠀⇒ Volume = 4/3 × π × (10)³

⠀⠀⠀⇒ Volume = 4/3 × π × 1000

Volume of the iron ball = 4/3 × π × 1000 cm³

Number of spherical balls = Volume of iron ball ÷ Volume of the spherical ball

⇒ 4/3 × π × 1000 ÷ 4/3 × π × 125

⇒ 1000 ÷ 125

⇒ 8

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Answer 2

Given :

Radius of a spherical ball = 5 cm

Radius of an iron ball = 10 cm

To find :

Number of spherical balls that can be made from the iron ball

Knowledge required :-

→ Formula of volume of sphere :-

Volume of sphere = 4/3πr³

where,

Take π = 22/7

r = radius

Solution :

Volume of the spherical ball :-

⠀⠀⠀⇒ Volume = 4/3πr³

⠀⠀⠀⇒ Volume = 4/3 × π × (5)³

⠀⠀⠀⇒ Volume = 4/3 × π × 125

Volume of the spherical ball = 4/3 × π × 125 cm³

Volume of the iron ball :-

⠀⠀⠀⇒ Volume = 4/3πr³

⠀⠀⠀⇒ Volume = 4/3 × π × (10)³

⠀⠀⠀⇒ Volume = 4/3 × π × 1000

Volume of the iron ball = 4/3 × π × 1000 cm³

Number of spherical balls = Volume of iron ball ÷ Volume of the spherical ball

⇒ 4/3 × π × 1000 ÷ 4/3 × π × 125

⇒ 1000 ÷ 125

⇒ 8

hope it's helpful to you