Question

Eight metallic spheres; each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere. 

Answer 1

Radius of metallic sphere = `2  mm = 1/5 cm`  

Volume = `4/3pir^3`

= `4/3 xx 22/7 xx 1/5 xx 1/5 xx 1/5`

= `88/(21 xx 125) cm^3`

Volume of 8 spheres = `(88 xx 8)/(21 xx 125)`

= `704/(21 xx 125) cm^3`  ...(1) 

Let radius of new sphere = R 

∴ Volume = `4/3piR^3`

= `4/3 xx 22/7R^3`

= `88/21R^3`   ...(2) 

From (1) and (2)  

`88/21R^3 = 704/(21 xx 125)` 

`=> R^3 = 704/(21 xx 125) xx 21/88 = 8/125` 

`=> R = 2/5 = 0.4  cm = 4  mm`