Question

metallic spheres of radius 6cm 8 cm and 10 cm respectively are melted to form a single solid spheres find the radius of the resulting sphere​

Answer 1

Step-by-step explanation:

According to question

3 metallic spheres are melted to form a single sphere.

so, Volume of resultant sphere=volume of first sphere+volume of 2nd sphere+volume of 3rd sphere

so, 4/3πr³=4/3π{ (6cm)³+(8cm)³+(10cm)³ }

r³ = 216cm³+512cm³+1000cm³

r³=1728cm³

r³=(12cm)³

r=12cm

Hence radius of resultant sphere is 12cm.

Answer 2

★Given:-

• Metallic spheres of radius 6cm 8 cm and 10 cm respectively.

• They are melted to form a single solid spheres.

★To find:-

• Radius of resulting sphere.

★Solution:-

Let,

• r1= 6cm

• r2= 8cm

• r3= 10 cm
• R = radius of new sphere

Using the formula,

✦Volume of sphere = 4/3πr³

Volume of 1st metallic sphere:-

⇒ (V1)= 4/3π(r1)³

⇒ 4/3 π (6)³

Volume of 2nd metallic sphere:-

⇒ (V2)= 4/3π(r2)³

⇒ 4/3 π (8)³

Volume of 3rd metallic sphere:-

⇒ (V3) = 4/3π(r3)³

⇒ 4/3 π (10)³

According to question,

As the spheres are melted to form a single solid sphere,

→Volume of 3 old spheres= volume of new sphere

→V1+V2+V3 = V  

Putting the values,

⇒4/3π(6)³+ 4/3π(8)³+4/3π(10)³=4/3πR³

⇒4/3π(6³+8³+10³)=4/3 πR³

⇒216+512+1000=R³

⇒1728= R³

⇒R= 12

Hence,

The radius of the resulting sphere = 12cm.

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