Question

the values of two sphere are in the ratio 125 : 27 find the differences of their surface areas in terms of pi the sum of the radius of the sphere is 8 cm

Answer 1

let the ratio of the volumes be
      R3/r3=125/27
so     R/r=5/3
the surface area=4 pie R2-4 pie r2
                             4 pie(R2-r2)
                             4 pie(16)   
                              64 pie
                                       

Answer 2

4/3πR1^3 : 4/3πR2^3 = 125: 27
R1/R2 = cube root (125/27) = 5/3

R1+R2 = 8
R1= 5/3R2

5/3R2+R2= 8

8R2/3= 8

R2 = 3

R1 = 5

Surface Area difference = 4π(R1^2 -R2^2)
= 4π(5^2-3^2) = 64π