Question

There are 3 spherical balls whose radius are 1/2 cm, 1/3 cm, 1/4 cm and melted to form a new spherical ball. What is the radius of new spherical ball?
1. (∛305)/12 cm
2. (∛306)/12 cm
3. (∛308)/12 cm
4. (∛307)/12 cm

Answer 1

Correct Answer - Option 4 : (∛307)/12 cm

Given:

The radius of spherical balls = 1/2 cm, 1/3 cm, 1/4 cm

Formula used:

The volume of sphere = (4/3)πr³

Calculation:

Let the radius of the new sphere be R and the radius of spherical balls be r1, r2 and r3.

So, r₁ =1/2 cm, r₂ = 1/3 cm, r₃ = 1/4 cm

According to the question,

The volume of 3 spherical balls = Volume of new spherical ball

⇒ (4/3)πr₁³ + (4/3)πr₂³ + (4/3)πr₃³ = (4/3)πR³

⇒ (4/3)π[r13 + r23 + r₃³] = (4/3)πR³

⇒ [(1/2)³ + (1/3)³ + (1/4)³] = R³

⇒ (1/8) + (1/27) + (1/64) = R³

⇒ R³ = (216 + 64 + 27)/1728

⇒ R³ = 307/1728

⇒ R = (∛307)/12 cm

∴ The radius of new spherical ball is (∛307)/12 cm.