Question

the surface area of a sphere is 576piecm2.what will be its volume?if it is melted how many small spheres of diameter 1 can be made out of it?

Answer 1

let us accept it as a solid sphere

When melted the volume remain the same.

Surface area 576pi = 4pir^2

=> r = sqrt(576/4) = 12 cm

V = 4/3*pi*r^3 = 4/3*pi*12^3

Let n be number of spheres to be produced

number = n

r = 1/2 cm

=> 4/3* pi*12^3 = n*4/3*pi * 1/8

=> n/8 = 12^3 => n = 8*12^3 = 13824

13824 small spheres can be made