Question

if three metallic sphere of redii 6cm,8cm and 10cm are melted to form a single sphere ,the diameter of the square is​

Answer 1

Answer:

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Answer 2

Answer:

The Diameter of the sphere is 24  cm

Among the given options option (b) 24 cm is the correct answer.

Step-by-step explanation:

Let r1, r2 ,r3 be the radius of the given 3 spheres & R be the radius of a single solid sphere.

Given :  

r1 = 6cm, r2 = 8 cm, r3 = 10 cm

 

Volume of first metallic sphere (V1) = 4/3π(r1)³  

V1 = 4/3 π (6)³

Volume of second metallic sphere (V2) = 4/3π(r2)³  

V2 = 4/3 π (8)³

Volume of third metallic sphere (V3) = 4/3π(r3)³  

V3 = 4/3 π (10)³

Volume of single solid sphere(V) = 4/3πR³

 

A .T.Q

Volume of 3 metallic spheres = volume of single solid sphere

V1 + V2 + V3 = V

4/3 π (6)³ + 4/3 π (8)³+ 4/3 π (10)³ = 4/3πR³

4/3π(6³+8³+10³) = 4/3 πR³

216 + 512 + 1000 = R³

1728 = R³

(12×12×12) = R³

12³ = R³

R = 12

Radius of the sphere = 12 cm  

Diameter of the sphere = 2 × Radius = 2 × 12 = 24 cm  

Hence, the Diameter of the sphere is 24  cm

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