Question

The sum of the surface areas of two spheres is 100 cm2 and
the ratio of their volumes is 64:27. What is the sum of the
radii of the spheres?

Answer 1

Answer:

Step-by-step explanation:

ratio of their volume  =  64 : 27

4/3 π R³  :  4/3 π r³      =  64 : 27

      R³  : r³   =  4³ : 3³

R  : r  = 4 : 3

given,

sum of the surface area  of two spheres  =  100 cm²

4πR²   + 4πr²   = 100

4π (16x ² + 9x²  )  = 100

22/7 (25x²)    = 100/4

  25 x²  = 25 ( 7/22)

     x²   = 7/22

       x  =  0.56

R = 4 (0.56)                r = 3(0.56)

   =2.24                         = 1.68

sum of the radii  = 2.24 + 1.68  = 3.92