Metallic spheres of radius 6 cm,8 cm, and 10 cm respectively aremelted

1.	Metallic spheres of radius 6 cm,8 cm, and 10 cm respectively aremelted to form a single solid sphere.Find the radius of the resultingsphere.t.
Answer» 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= 8cm, r3= 10 cm Volume of first metallic sphere (V1)= 4/3π(r1)³ = 4/3 π (6)³ Volume of second metallic sphere (V2)= 4/3π(r2)³ = 4/3 π (8)³ Volume of third metallic sphere (V3) = 4/3π(r3)³ = 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 Hence, the radius of the resulting sphere = 12 cm Hit like if you find it useful!

Metallic spheres of radius 6 cm,8 cm, and 10 cm respectively aremelted to form a single solid sphere.Find the radius of the resultingsphere.t.

Answer»

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= 8cm, r3= 10 cm

Volume of first metallic sphere (V1)= 4/3π(r1)³ = 4/3 π (6)³

Volume of second metallic sphere (V2)= 4/3π(r2)³ = 4/3 π (8)³

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

Hence, the radius of the resulting sphere = 12 cm

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