Question

three spheres of radii 3cm,4cm and 5cm are melted together to form a single sphere.find the radius of new sphere.

Answer 1

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RADIUS OF NEW SPHERE= CUBE ROOT OF (R13+R23+R33)


= CUBE ROOT OF(27+64+125)


= CUBE ROOT OF 216


= 6 CM IS THE RADIUS OF THE NEW SPHERE

Answer 2

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.