Question

Twenty-seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S′. Find the (i) radius r′ of the new sphere,  (ii) ratio of S and S′​

Answer 1

Answer:

(i) radius r′ of the new sphere is 3r

 (ii) ratio of S and S′​ is 1: 9

Step-by-step explanation:

(i) Radius of 1 solid iron sphere =r

⇒Volume = 4/3π$r^3$

⇒Volume of 27 solid iron spheres =27× 4/3π$r^3$

⇒ 4/3πr′^3 =27× 4/3π$r^3$  

$r'^3$ =2π$r^3$

⇒r′ =3r

(ii) Surface area =4π$r^2$

SA r′ =4π$r'^2$

=4π$(3r)^2$

=36π$r^2$  

S/S′=4π$r^2$ /36π$r^2$  = 1/9 = 1: 9