Frustum of a Cone Total Surface Area

We come across many objects in our daily lives that require us to determine their volume and surface areas. For instance, we may need to figure out how much water a tank can store. We’ll need to know the tank’s shape and how to compute its volume to do so. Some solids are made up of various standard forms. The majority of objects were made up of a combination of these shapes. However, by eliminating a part of a solid, we can sometimes create a new shape. So let’s discuss the total surface area of the frustum of a right circular cone in detail. 

Cone: Definition

A cone is a solid whose base is bordered by a simple closed curve but whose curved surface tapers to a point opposite the base termed the vertex. The cone is called a circular cone if the base is round.

The perpendicular height, often known as the height of a cone, is the distance between the vertex and the base of the cone. The distance between the vertex and the circumference of the base seems to be the slant height of a right circular cone.

Slice a right circular cone or a pyramid along a plane parallel to the solid’s base. A frustum of a solid is the piece of concrete that remains between the parallel cutting plane and the base of the cone or pyramid. The Latin term frustum implies ‘piece’ and ‘crumb.’

Total Surface Area of a Cone: The surface area of the cone is equal to the area of the circular base plus the lateral surface area.

As a result, the total surface area of a frustum of a right circular cone is πr(l+r) = πr^2 + πrl square units. 

Frustum of a Cone

A frustum is a solid object formed by cutting a cone or a pyramid from the top down. It’s the part of the cone or pyramid between the base and the plane parallel to it. 

It’s a three-dimensional figure made out of other three-dimensional figures, such as a cone or a pyramid. The height of a frustum is dictated by the radius of base 1 (top) and the radius of base 2 (bottom). 

Types of Frustum

A frustum is a three-dimensional shape enclosed between two parallel planes of a solid divided into two halves. In general, there seem to be two types of frustum:

Cone frustum: Cut the cone at the vertex or apex to make it. To make a frustum, a plane parallel to the base of the cone cuts the top of the cone or the apex. It’s also known as a truncated cone or even a frustum of a cone.

Pyramid frustum: The pyramid’s apex was chopped with a plane parallel to the base, resulting in this shape. The pyramid’s base can be either a triangle or a square in this case. As a result, frustum could be made from triangular or square pyramids.

Frustum of a Cone Examples

A cone’s frustum can be seen in a variety of situations. Buckets, table lamp shades, and even glass tumblers appear to be great examples.

Frustum of a cone total surface area formula

πl [ (R^2 – r^2) / r ] + π (R^2 + r^2): total surface area of frustum of a cone formula

Conclusion

The Latin phrase frustum means “cut off a piece.” Frusta is the plural form. The frustum of a cone is the section of a cone that forms when a cone is planned into two parts. The upper half of the cone keeps its shape, but the lower half becomes a frustum. To obtain this piece, the right circular cone should be split horizontally, parallel to the base. Both of these books are divided into several sections and volumes. The pointed part of a glass tumbler is removed, giving it the appearance of a cone. A tumbler’s frustum can be compared to the frustum of a cone. I hope now you got all the necessary information regarding the total surface area of the frustum of a right circular cone.