Question

The radius of a metallic sphere is 9 cm. It was melted to make a wire of diameter 4 mm. Find the length of the wire.

Answer 1

Hi ,

1 ) Radius of the metallic Sphere ( R )

= 9 cm

If it is melted and cast into a wire ,

Diameter of the wire ( d ) = 4 mm

Radius of the wire ( r ) = d/2

r = 4/2 = 2 mm = ( 2/10 )cm

r = 1/5 cm

let the length of the wire = h cm

Volume of the wire = volume of the

Sphere

πr² h = ( 4πR³)/3

h = ( 4πR³ )/(3πr² )

h = ( 4R³ )/3r²

h = ( 4 × 9 × 9 × 9 )/(3 × 1/5 × 1/5 )

h = ( 4 × 9 × 9 × 3 × 5 × 5 )

h = 24300 cm

Therefore ,

Length of the wire = h = 24300cm

I hope this helps you.

: )

Answer 2

Heya !!



Radius of metallic sphere ( R ) = 9 cm



Therefore,


Volume of metallic sphere = 4/3 πR³




=> 4/3 × 22/7 × 9 × 9 × 9




=> ( 4 ×22 × 3 × 9 × 9 ) / 7



=> 21384/7 cm³.




Diameter of wire ( D ) = 4 mm



Radius ( R 1 ) = D/2 = 4/2 = 2 mm = 2/10 cm = 1/5 cm.



Therefore,



Volume of wire = πR²H


=> 22 / 7 × 1/5 × 1/5 × H



=> ( 22 × 1 × 1 × H ) / ( 7 × 5 × 5 )



=> 22H/175



Volume of metallic sphere = Volume of wire



21384/7 = 22H/175



22H = ( 21384 × 175)/7



22H = 534600


H = 534600/22 = 24300 cm.


Hence,



Length of wire = H = 24300 cm.