**Question 1.** **Asked on :**19 January 2019:10:07:46 AM

Three spheres having radii 2 cm ,3 cm and 5 cm are melted together to from a single find the radius of the new sphere.

*-Added by Prince Rawat*

**Answer:**

Let three spheres are S1, S2 & S3

having radii r₁ = 3cm, r₂ = 4cm & r₃ = 5cm respectively.

Let the radius of new Big sphere S is R.

A/Q,

Volume of new Sphere S = Sum of volumes three Spheres S1, S2 & S3

⇒ 4/3πR³ = 4/3π(r₁)³ + 4/3π(r₂)³+4/3π(r₃)³

⇒ 4/3πR³ = 4(r₁³ +r₂³ + r₃³)/3π

⇒ R³ = r₁³ +r₂³ + r₃³

⇒ R³ = 3³ +4³ + 5³ = 27 + 64 + 125

⇒ R³ = 216

⇒ R = ∛216

⇒ R = 6cm

Therefore radius of new Sphere is 6 cm.

*-Answered by Himanshi Verma* On 20 January 2019:05:15:36 PM

**Answer:**

Let three spheres are S1, S2 & S3

having radii r₁ = 3cm, r₂ = 4cm & r₃ = 5cm respectively.

Let the radius of new Big sphere S is R.

A/Q,

Volume of new Sphere S = Sum of volumes three Spheres S1, S2 & S3

⇒ 4/3πR³ = 4/3π(r₁)³ + 4/3π(r₂)³+4/3π(r₃)³

⇒ 4/3πR³ = 4(r₁³ +r₂³ + r₃³)/3π

⇒ R³ = r₁³ +r₂³ + r₃³

⇒ R³ = 3³ +4³ + 5³ = 27 + 64 + 125

⇒ R³ = 216

⇒ R = ∛216

⇒ R = 6cm

Therefore radius of new Sphere is 6 cm.

*-Answered by Master Purushottam* On 24 August 2019:12:18:19 AM

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