Question

A solid sphere of radius 6 meter is melted and recast into some small sphere of radius as 3, 2 and 1 meter. If the numbers of spheres of different radius are the same then find how many small spheres were made?
1. 12
2. 4
3. 5
4. 6
5. 10

Answer 1

Correct Answer - Option 4 : 6

GIVEN:

Radius of big sphere = 6 m

Radius of small sphere’s = 1 m, 2 m & 3 m

CONCEPT:

“Since the given sphere is a solid sphere which means that it is also filled inside. so we can say that the volume of the bigger sphere will be equal to the volume of the small sphere.”

CALCULATION:

So we can write it as,

⇒ 4/3πR³ = N [4/3πr₁³+ 4/3πr₂³+ 4/3πr₃³]      [N = number of spheres]

⇒ 4/3 πR³ = N 4/3π [r₁³ + r₂³ + r₃³]

⇒ Here R = 6m, r₁ = 1m,  r₂ = 2m  , r₃ = 3m

⇒ R³ = N [r13 + r23 + r33]

⇒ 216 = N [1 + 8 + 27]

⇒ N = 216/36 = 6