A sphere and a cone have the same radius. If the volume of the sphere is half of the volume of the cone, find the ratio of the height and radius of the cone.


  1. Home
  2. Math
  3. All Questions
Answer:

8:1

Step by Step Explanation:
  1. We know that the volume of a cone with radius r and height h =  
    1
    3
     πr2h.
  2. We also know that the volume of a sphere with radius r =  
    4
    3
     πr3.
  3. We have been told that the volume of the sphere is half the volume of the cone.
    Therefore,  
    4
    3
     πr3 =  
    1
    2
      × ( 
    1
    3
     πr2h)
    or,  
    h
    r
      = 8:1
  4. Thus, the ratio of the height and radius of the cone is 8:1.

You can reuse this answer
Creative Commons License