Question

27 solid iron spheres each of radius 'r' and surface area S are melted to form a sphere with surface area S' find the

1] radius r' of new sphere
2] ratio of S and S'

Answer 1

Answer:

Step-by-step explanation:

(i)Radius of 1 solid iron sphere = r

Volume of 1 solid iron sphere = (4/3) πr3

Volume of 27 solid iron spheres = 27x (4/3) πr3

27 solid iron spheres are melted to form 1 iron sphere. Therefore, the volume of this iron sphere will be equal to the volume of 27 solid iron spheres. Let the radius of this new sphere be r'.

Volume of new solid iron sphere = (4/3) πr'3

A/q

4/3 πr'3= 36πr³

r'³= 27r³

r'³= (3r)³

r′ = 3r.......

(ii) Surface area of 1 solid iron sphere of radius r = 4πr2, Surface area of iron sphere of radius r' = 4π (r')2 = 4 π (3r)2 = 36 πr2

Required ratio = S:S′

= 4πr²:36πr² = 1:9

Hence, the ratio of S & S' = 1:9