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 = 8373.33 Input: 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.
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
- Percentage increase in volume of the sphere if radius is increased by a given percentage
- Largest right circular cone that can be inscribed within a sphere
- Largest right circular cone that can be inscribed within a sphere which is inscribed within a cube
- Largest sphere that can be inscribed within a cube which is in turn inscribed within a right circular cone
- Calculate volume and surface area of a cone
- Program for Volume and Surface area of Frustum of Cone
- Calculate Volume and Surface area Of Sphere
- Volume of largest right circular cylinder within a Sphere
- Volume of biggest sphere within a right circular cylinder
- Radii of the three tangent circles of equal radius which are inscribed within a circle of given radius
- Python | Percentage increase in hemisphere volume if radius is increased
- Percentage change in Hemisphere volume if radius is changed
- Maximum area of a Rectangle that can be circumscribed about a given Rectangle of size LxW
- Largest cone that can be inscribed within a cube
- Largest cube that can be inscribed within a right circular cone
- Largest right circular cylinder that can be inscribed within a cone
- Largest right circular cylinder that can be inscribed within a cone which is in turn inscribed within a cube
- Largest cube that can be inscribed within the sphere
- Largest sphere that can be inscribed inside a cube
- Largest sphere that can be inscribed in a right circular cylinder inscribed in a frustum
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.