The diameter of a metallic sphere is equal to 9 cm. It is melted and d

1.	The diameter of a metallic sphere is equal to 9 cm. It is melted and drawn into a long wire of diameter 2 mm having uniform cross-section. Find the length of the wire.
Answer» Given, Radius of the sphere = 9/2 cm So, its volume = 4/3 πr³ = 4/3 π(9/2)³ And, the radius of the wire = 2 mm = 0.2 cm Let the length of the wire = h cm So, the volume of wire = πr²h = π(0.2)²h Then, according to the question we have Volume of wire = Volume of sphere π(0.2)²h = 4/3 π(9/2)³ h = 4 x 729/ (3 x 8 x 0.01) = 12150 cm Therefore, the length of the wire = 12150 cm

The diameter of a metallic sphere is equal to 9 cm. It is melted and drawn into a long wire of diameter 2 mm having uniform cross-section. Find the length of the wire.

Answer»

Given,

Radius of the sphere = 9/2 cm

So, its volume = 4/3 πr³ = 4/3 π(9/2)³

And, the radius of the wire = 2 mm = 0.2 cm

Let the length of the wire = h cm

So, the volume of wire = πr²h = π(0.2)²h

Then, according to the question we have

Volume of wire = Volume of sphere

π(0.2)²h = 4/3 π(9/2)³

h = 4 x 729/ (3 x 8 x 0.01) = 12150 cm

Therefore, the length of the wire = 12150 cm