if two spheres of same diameter is melted & made into one big sphere then the radius of the new sphere is

Question

i can't understand for this question. please give me a explain and answer for this question.

Answer 1

The volume of a sphere is 4/3*pi*r³

 

Two such spheres would have a volume of 2*4/3*pi*r³  = 8/3*pi*r³ 

 

let the radius of the new sphere be R

 

Then 4/3*pi*R³ =  8/3*pi*r³

 

R³ = 2r³

 

R = (2)^1/3 *r  = 1.26*r

 

Therefore the radius of the new sphere is 1.26 times the radius of the first sphere