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.
Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.
- 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
- Calculate volume and surface area of a cone
- Program for Volume and Surface area of Frustum of Cone
- Volume of biggest sphere within a right circular cylinder
- Volume of largest right circular cylinder within a Sphere
- Calculate Volume and Surface area Of Sphere
- Largest sphere that can be inscribed within a cube which is in turn inscribed within a right circular cone
- Largest right circular cone that can be inscribed within a sphere which is inscribed within a cube
- Percentage change in Hemisphere volume if radius is changed
- Python | Percentage increase in hemisphere volume if radius is increased
- Radii of the three tangent circles of equal radius which are inscribed within a circle of given radius
- Area of square Circumscribed by Circle
- Area of a Circumscribed Circle of a Square
- Side of a regular n-sided polygon circumscribed in a circle
- Largest cone that can be inscribed within a cube
- Largest right circular cylinder that can be inscribed within a cone
- Largest cube that can be inscribed within a right circular cone
- Mensuration 3D- Hollow sphere
- Largest cube that can be inscribed within the sphere
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.