If a solid sphere of radius 10 cm is moulded into 8 spherical solid ba

1.	If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the radius of each such ball is ___________.1. 1.25 cm2. 2.5 cm3. 3.75 cm4. 5 cm
Answer» Correct Answer - Option 4 : 5 cm Given: Radius of a solid sphere = 10 cm Number of solid spherical balls = 8 Concept Used: For number of balls we have to equate the volume of all the balls and the solid sphere volume Formula Used: Volume of a sphere = (4/3)πr³, here r = Radius of the sphere Calculation: Let radius of a solid spherical ball be R cm (4/3)π(10 cm)³ = 8 × (4/3)πR³ ⇒ R³ = 1000/8 ⇒ R3 = 125 ⇒ R = 5 Radius of a spherical ball = 5 cm ∴ The radius of each small spherical ball is 5 cm

If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the radius of each such ball is ___________.1. 1.25 cm2. 2.5 cm3. 3.75 cm4. 5 cm

Answer» Correct Answer - Option 4 : 5 cm

Given:

Radius of a solid sphere = 10 cm

Number of solid spherical balls = 8

Concept Used:

For number of balls we have to equate the volume of all the balls and the solid sphere volume

Formula Used:

Volume of a sphere = (4/3)πr³, here r = Radius of the sphere

Calculation:

Let radius of a solid spherical ball be R cm

(4/3)π(10 cm)³ = 8 × (4/3)πR³

⇒ R³ = 1000/8

⇒ R3 = 125

⇒ R = 5

Radius of a spherical ball = 5 cm

∴ The radius of each small spherical ball is 5 cm

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