# 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

18 views
in Aptitude
closed
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

by (45.3k points)
selected by

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.