Minimum volume of cone that can be circumscribed about a sphere of radius R
Given a sphere of radius R, The task is to find out the minimum volume of the cone that can be circumscribed about it.
Input: R = 10 Output: Volume of cone = 8373.33 Explanation: Radius of cone = 14.14 and Height of cone = 40, Volume of cone = So, volume = 8373.33Input: R = 4 Output: Volume of cone = 535.89
we have given a sphere of radius R inscribed in Cone. We need to find out the radius and height of the cone to find out the volume of the cone.
- In triangle AOE and ALC compute sin(X) i.e. For triangle AOE and for triangle ALC
- Now, From equating both we get
- Insert the value of H in Volume i.e. and for volume to be minimum .
- From the above equation we get and putting this value in H we get
- Hence, applying the formula of volume of cone and putting and we get the desired result.
Time complexity: O(1) since performing constant operations
Auxiliary space: O(1) since using constant variables