Question

If 3 spherical balls having radius 6 cm, 8 cm and 10 cm respectively are melt together to form a big spherical ball. What is the total surface area of the big spherical ball?
1. 548π cm²
2. 576π cm²
3. 672π cm²
4. 786π cm²

Answer 1

Correct Answer - Option 2 : 576π cm²

Given:

The radius of 3 small spherical ball = 6 cm, 8 cm and 10 cm

Concept used:

The volume of 3 spherical melted balls = Volume of 1 big spherical ball

Formula used:

The volume of sphere = (4/3) × π × r3

where,

r →  Radius of the sphere

The volume of big sphere = (The volume of the first sphere + The volume of the second sphere + The volume of the third sphere)

Calculations:

According to the question, we have

The volume of sphere = (4/3) × π × r3

The volume of the big ball = {(4/3) × π × (6)³} +  {(4/3) × π × (8)³} + {(4/3) × π × (10)³}

⇒ (4/3) × π × r3 = (4/3) × π × (216 + 512 + 1000)

⇒ r³ = 1728

⇒ r = 12

Now,

The total surface area of the big spherical ball = 4πr²

⇒ 4π × (12)²

⇒ 4π × 144

⇒ 576π

∴ The total surface area of the big spherical ball is 576π cm².