Frustum of a Cone Slant Height

Cone is a shape that we read in the books of geometry or mathematics. Because a cone is a shape, it’s not new to us. Usually, we observe several things around us in a day whose shape is conical. Yes, we are going to discuss that in this article. We shall discuss the shape of the cone, the frustum of a cone slant height formula, and the slant height of the frustum of a cone in detail in the article.  If you are preparing for geometry and mathematics, then you will enjoy reading this article for sure. Let us read more about it in detail. 

Frustum of a Cone Slant Height:

When you cut a cone into two parts by a plane, the frustum is obtained. Imagine the shape or structure of a cone. When you cut the cone into two parts from the horizontal plane then, the upper part of the cone will remain the cone. It means the shape of the upper part of the cone will not change, it will still look like a cone, but the size will be reduced. At the same time, the bottom part of the cone will not look like a cone after cutting from the plane. The lower or bottom part of the cone will look like a frustum. Yes, that is known as a frustum. But you should remember before considering that a part of cone frustum is the plane of cutting. The frustum of a cone slant height can be obtained only when the cone is cut into two parts from the horizontal plane or parallel to the base. In simple words, when a plane that is parallel to the base of the cone cuts the cone into parts, then the frustum is obtained. The part in which the base of the cone remains is considered frustum or the bottom part of the cone. 

Frustum of a cone slant height formula:

The formula evaluates the volume of a circular cone. 

The volume of a circular cone is equal to πr^2(h/3). 

In which π is equal to 22/7 or 3.14. r signifies the radius, and h signifies the height. 

So for calculating the volume of a frustum cone slant height, firstly, we have to calculate the volume of an original cone and the volume of a sliced cone. After calculating the volume of the sliced upper part of the cone and the original cone, the subtraction is done between the values of the volumes, and this is how the volume of the frustum is calculated. 

The volume of the frustum and the original cone is equal and minus the volume of the sliced upper part of the cone. 

The formula for calculating the value of the volume of a frustum is the

V = [πh/3 (R^2 + Rr + r^2)]. 

Besides it, by the formula V = [πh/3 {(R^3 – r^3)/3}] also, you can calculate the volume of the frustum. 

Here in these formulas, R denotes the radius of the base circle of the frustum. 

R denotes the radius of the upper circular surface of the frustum. 

If we focus on the dimensions of the frustum, then mainly there are four dimensions of the frustum. The first of them is the radius of the upper circular surface of the frustum. The second is the radius of the base of the frustum. The third is the height of the frustum, and the fourth is the slant height of the frustum. 

We can calculate the volume of frustum by using another formula also. In this formula, firstly, we have to calculate the surface area of both bases of the frustum. The surface area of the upper circular base or surface and the surface area of the lower base of the frustum is obtained. Both bases of the frustum are Circular, so their surface area is obtained by the formula of the surface area of a circle. Then by using the measurements of dimensions, you can calculate the volume of the frustum. 

The frustum volume is calculated by this formula also V =H/3(S1+S2+√S1S2).

Here S1 is the surface area of the upper base. 

S2 is the surface area of the lower base. 

H is the height, which is the distance between both bases. 

Conclusion: 

This article was about frustum. The frustum is a shape in geometry or mathematics. The cone obtains the frustum. When you cut a cone into two parts by the horizontal plane, frustum is obtained. There are many uses of the frustum in our daily life, as the bucket we use in the bathroom is frustum in shape. We have discussed the dimensions of frustum also. In detail, we discussed the slant height of a frustum of a cone and the frustum of a cone slant height formula. I hope the article is helpful for you.