Ahollow ball is made of rubber that is 2 cm thick. the ball has a radius to the outside surface of 6 cm.
what is the approximate volume of rubber used to make the ball?
use 3.14 to approximate pi.

33.5 cm³

267.9 cm³

636.4 cm³

904.3 cm³

•  thickness of the hollow ball:   t = 2 cm;

•  radius to the outside surface:  R = 6 cm;

•  radius to the inside surface:

   r = R – t

   r = 6 – 2

   r = 4 cm.

The answer you're looking for is the difference between the volume of two spheres:

•  Volume of a sphere whose radius is  R = 6 cm:
 
               4π · R³
   V₁  =  —————
                   3

               4 · 3.14 · 6³
   V₁  ≈  ———————
                       3

               4 · 3.14 · 216
   V₁  ≈  ————————
                        3

               2712.96
   V₁  ≈  ——————
                    3
  
  V₁ ≈ 904.32 cm³          (i)

•  Volume of a sphere whose radius is  r = 4 cm:
 
               4π · r³
   V₂  =  —————
                    3

               4 · 3.14 · 4³
   V₂  ≈  ———————
                       3

               4 · 3.14 · 64
   V₂  ≈  ———————
                       3

               803.84
   V₂  ≈  —————
                    3
  
  V₂ ≈  267.95 cm³          (ii)

—————

So the volume of rubber used is

V = V₁ – V₂

V ≈ 904.32 – 267.95

V ≈ 636.37 cm³

V ≈ 636.4 cm³   <———   this is the answer  (3rd option)

I hope this helps. =)

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