In three-dimensional geometry, most of the people have learned to find out the volume of different 3D shapes like cones, cylinders etc. But they are not aware of finding the volume and area of a frustum of a solid (usually cone or a pyramid). The word “frustum” means to cut off. It means that a part of a cone or a pyramid that remains after cutting off by a plane parallel to its bases. When you consider the right circular cone, the bottom of the cone is perfectly circular in shape. Now, if the plane cuts anywhere or the tip of the cone parallel to the base and perpendicular to the height, you will get two portions. The portion that lies between the base and the parallel plane is commonly called the frustum of a cone. You can easily find the volume of a frustum by subtracting the volume of the smaller portion from the volume of the larger portion of a cone.
We know that the volume of the cone is (⅓) πr2h
So, the frustum volume is given as (⅓) π H (R2 + Rr + r2)
Where,
The notation “R” and “r” are the radius of the cone and the sliced out cone respectively
“H” is the height of the frustum. (i.e., Height of cone – Height of the sliced out cone)
The height of the frustum of a cone is concluded with the help of similar triangle properties since it is the process of slicing a similar triangle from a cone. When you look at the frustum formula, it is quadratic in nature. You can directly apply the radius value to find the volume or else you can simplify the quadratic part of the formula. With the help of quadratic equations, you will find the root values which is called as the quadratic equation solution. Similarly, you can find the frustum for any solid by cutting off with a plane parallel to the base. Once you know about the combination of shapes of a solid, you can easily find the volume and surface area.
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