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 Mathematics » SURFACE AREAS AND VOLUMES
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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