Conical Frustum Formulas – Slant height,Volume, Lateral, Base and Total surface areas
Frustum of A Cone
When cut, the lower part of the right circular cone is called a frustum. We need to cut the right circular cone with a to cut it horizontally or parallel to the base of the cone, then the solid shape between the base and plane of the cone is called the frustum of a cone.
Formulas of Right Circular Cone
The volume of a Cone = V
Base Area of a cone
Lateral surface area of a cone
The total Surface area of a cone
The slant height of a cone
Frustum of cone formulas – Volume of a Frustum of Cone
The volume of a frustum can be defined as the quantity of matter that it can hold in the space that is present inside it .
Frustum of a cone of altitude “h” with a large base radius “R” and small base radius “r” . Slant heights “s” of the frustum and the cone.
Altitude ( h) is the perpendicular distance between the bases of a frustum of a cone.
Volume of a Frustum of a Cone
Frustum volume can be calculated using its height and the areas of its bases. Let us consider a frustum large base areas “B1” and a small base area “B2” and height “h” and. Then its volume is calculated by using the following formula
Volume of a Frustum of a Cone
Generator or Slant height of frustum of cone formula
The distance measured along the lateral face of the frustum is called the slant height of the same
The Slant of the Frustum of a Cone (S)
R= The radius of the cone (large base radius)
r= the radius of the Frustum cone (small base radius)
h= height of the Frustum cone
Slant height and Height of the cone which the frustum is a part of that cone.
The slant height of the cone of which the frustum is a part =
Height of the cone of which the frustum is a part =
Frustum of cone formulas – Surface area of a Frustum of Cone
What Is the Surface Area of Frustum?
The surface area of a frustum area is calculated by the sum of the areas of its faces and is measured in square units.
With respect to the frustum, there are two types of surface areas.
1. Lateral Surface Area (LSA) or Curved Surface Area (CSA) for the frustum of a cone
2. Total Surface Area (TSA) for the frustum of a cone.
The curved surface area or lateral surface area of a frustum of a cone is the area of its curved face.
Frustum of a cone of height “h” with a large base radius “R” and small base radius “r” and “s” slant height of the frustum.
The curved surface area of a frustum of cone formula ( LSA or CSA)
The slant height of the frustum =
The curved (or lateral) surface area of any frustum can be calculated using the circumferences (or perimeters) of the bases and the slant height.
C1 is the circumference (or perimeter) of one base of the frustum, C2 is the circumference (or perimeter) of another base of the frustum, and slant heights “s” frustum and the cone, respectively. Then
The lateral (or curved) surface area of a frustum
The total surface area (TSA) of a frustum of a cone is obtained by adding the areas of both bases and its lateral (or curved) surface area.
Total surface area (TSA) of a frustum
Slant height of the a frustum =
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