Question

If 3 small spherical balls having radius 3 cm, 4 cm, and 5 cm melt together to form a big spherical ball. What is the radius of big spherical ball?
1. 8 cm
2. 7 cm
3. 6 cm
4. 9 cm

Answer 1

Correct Answer - Option 3 : 6 cm

Given:

Radius of 3 small spherical balls are 3 cm, 4 cm and 5 cm respectively.

Concept used:

Volume of 3 small spherical melted balls = Volume of 1 big spherical ball

Formula used:

Volume of sphere = (4/3) × π × r³

where,

r = Radius of sphere

Calculations:

Volume of sphere = (4/3) × π × r3

Volume of first small ball = (4/3) × π × (3)3

⇒ (4/3) × π × 27

⇒ 36π cm3

Volume of second small ball = (4/3) × π × (4)3

⇒ (4/3) × π × 64

⇒ 256π/3 cm3

Volume of third small ball = (4/3) × π × (5)3

⇒ (4/3) × π × 125

⇒ 500π/3 cm3

Volume of big ball = (4/3) × π × R3

Total volume of small balls = 36π + (256π/3) + (500π)/3

⇒ (108π + 256π + 500π)/3

⇒ 864π/3

⇒ 288π cm³

Volume of 3 small spherical melted balls = Volume of 1 big spherical ball

⇒ 288π = (4/3) × π × R3

⇒ R³ = 216

⇒ R = ∛216

⇒ R = 6 cm

∴ The radius of big spherical ball is 6 cm.