Question

the diameter of a copper sphere is 18cm.it is melted and drawn into a wire of 0.4cm in diameter. calculate the length of the wire in metres​

Answer 1

Answer:

$\bigstar{\bold{Length\:of\:wire=243\:m}}$

Explanation:

$\Large{\underline{\underline{\it{Given:}}}}$

• Diameter of sphere (D) = 18 cm
• Diameter of wire (d) = 0.4 cm

$\Large{\underline{\underline{\it{To\:Find:}}}}$

• Length of the wire in m

$\Large{\underline{\underline{\it{Solution:}}}}$

→ It is given that the sphere is made into a wire. Here wire is in the shape of a cylinder.

→ Hence,

  Volume of sphere =  Volume of cylinder

→ The radius of the sphere (R) = 18cm/2 = 9 cm = 0.09 m

→ The radius of the wire (r) = 0.4cm/2 = 0.2 cm = 2 × 10⁻³m

→ We know that volume of a sphere is given by

 Volume of sphere = 4/3 × π × r³

→ Volume of a cylinder is given by

 Volume of cylinder = π r² h

→ By given,

  4/3 π R³ = π r² h

→ Cancelling π on both sides,

   4/3 R³ = r² h

→ Substituting the radii

   4/3 × 0.09 × 0.09 × 0.09 = ( 2 × 10⁻³)² × h

→ 9.72 × 10⁻⁴ = 4 × 10⁻⁶ × h

  h = 9.72 × 10⁻⁴/4 × 10⁻⁶

  h = 2.43 × 10²

  h = 243 m

→ Here height of the wire is the length of the wire.

→ Hence the length of the wire is 243 m

$\boxed{\bold{Length\:of\:wire=243\:m}}$

$\Large{\underline{\underline{\it{Notes:}}}}$

→ The volume of a sphere is given by

  Volume of a sphere = 4/3 π r³

→ The volume of a cylinder is given by

   Volume of a cylinder = π r² h