Question

A wire of radius 3.0mm and length 200m is melted into a sphere. calculate the radius of the sphere in meters

Answer 1

Given:

➜ radius of wire, r = 3 mm

➜ length of wire, l = 200 mm

To Find:

➜ radius ( R ) of the sphere formed by melting the wire

Solution:

➜ Volume of Wire = Volume of Sphere { because matter would be same }

☛ πr²l = (4πR³)/3

cancel π both sides,

☛ r²l = 4R³ / 3

☛ 3r²l = 4R³

☛ R³ = (3r²l)/4

☛ R³ = 3×3×3×200/4

☛ R³ = 27 × 50

☛ R³ = 1350

☛ R ≈ 11.05

R = 11.05 mm

Divide by 1000 to get it in metres

R = 0.1105 m

Hence, Radius of the sphere is ≈ 0.1105 m