Question

Twenty seven solid iron spheres of radius r and surface area s are melted to form the sphere with surface area S'. find the
radius of the new sphere and ratio of s​

Answer 1

Answer:

I hope this answer is correct. The answer is radius of new sphere =3r and ratio of s is 1/9

Step-by-step explanation:

Let r1 be the radius of the first sphere and r2 be the radius of the second (new sphere)

Volume of 27 spheres =Volume of new sphere

27×4/3πr1^3 =4/3πr2^3

After cancellation

27r1^3=r2^3

r2=cube√27r1^3

r2=3r1

Ratio of surface area of one sphere to the surface area of new sphere will be

s/S'=

4πr1^2/4πr2^2

4 and π gets cancelled and we proved that r2=3r1 so

r1^2/(3r1^2)

r1^2/9r1^2

r1^2 gets cancelled so

1/9