Surface are of a sphere ( the globe in this case) is given by:-
#color(red)(S = 4*pi*r^2)# where #r# is radius of sphere.
The volume of a sphere is given by:-
#color(red)(V = 4/3*pi*r^3)# where #r# is the radius of sphere.
Given that #pi = 3#.
Surface area is #2700 cm^2#.
#therefore# #4*pi*r^2 = 2700#
#=> 4*3*r^2 = 2700#
#=>r^2 = 2700/(3*4) = 900/4#
#=> r = sqrt(900/4) = 30/2 = 15cm#.
Method 1.
Now volume is #4/3*pi*r^3#
#therefore# #V = 4/3*3*15^3 = 4*3375 = 13500cm^3#
Method 2.
#S = 4*pi*r^2# ------------------(1.)
#V = 4/3*pi*r^3# ------------------(2.)
Dividing equations (1.) & (2.)
#S/V = (4*cancelpi*r^2)/(4/3*cancelpi*r^3) = 3/r#
#=> S/V = 3/r#
#=> V = (S*r)/3 = (2700*15)/3 = 13500cm^3 #
