A solid sphere of radius r fits inside a hollow cylinder. The cylinder has the same internal diameter and length as the diameter of the sphere. The volume of a sphere is ⁴⁄₃ πr³ , where r is the radius of the sphere.
What fraction of the space inside the cylinder is taken up by the sphere?

Answer:

20) D

Diameter of sphere = r x 2 = d

Height (or length) of cylinder = d

Radius of cylinder = r

Volume of cylinder = πr²h = πr²d

We need to find the fraction of space taken by the sphere

  ⁴⁄₃ πr³  
   πr²d

  ⁴⁄₃ r  
    d

Since d = 2r,

  ⁴⁄₃ r  
   2r

  ⁴⁄₃   
   2

⁴⁄₃ ÷ 2 =  ⁴⁄₃ x  ¹⁄₂ = ⁴⁄₆ = ²⁄₃