Curved Surface Area & Volume of a Cone Formula

Surface area of a cone formula

A cone is a popular geometrical shape with a flat surface that tapers to appoint on another side. Cone can be of different types but we will focus on right circular cone throughout this article. This is the cone with a flat surface tapers to appoint that is angled at 90-degree from the midpoint of a circle.

In other words, the cone is the 3-dimensional structure with a circular base, a set of segments of lines that is connecting all the points together on the base with a common focused point i.e. apex. Thus, a cone can be seen as the set of non-congruent discs that are circular and stacked over one another where the radius of the adjacent disc would remain the constant.

A cone can also be taken as the triangle that is rotated along one of its vertices. There are a predefined set of basic cone formulas that are used to calculate its curved area, surface area, the volume of a cone, total surface area etc.

The curved surface area of a cone is the multiplication of pi, slant height, and the radius. Further, the surface area of a cone is given as the sum of the base and curved surface area. In mathematics, there is a special formula to figure it out –

\[\large Surface\;Area\;of\;cone=\pi r \left (s+r \right )\]

Where,
r is the radius of cone.
h is the height of cone.
s is the slant height of the cone.

Where r is the radius, s is the slant height and value of π is constant = 3.14

For a better understanding of cone formulas, you must have good knowledge of basic terminologies like radius, height, slant height etc. Radius is the distance from the centre to the edge of the circle till the end. Height is the distance from the centre point to the top of the cone. The slant height is the length from the tip of the cone to the edge of the cone. Pi (π) is a special term that is used along with the circles whose value is constant i.e. 3.14. wherever, you see the symbol (π) in mathematics, put the value 3.14 against it to solve an equation.

Volume of a Cone formula

There is used a special formula to find the volume of the cone. The volume gives you an idea of how much space will be taken inside the cone. The final answer would be express in terms of cubic units. In mathematics, the volume of a cone formula is given as –

\[\large Vomule\;of\;cone=\frac {1}{3}\pi r^{2}h\]

Where,
r is the radius of cone.
h is the height of cone.

Where r is the radius, s is the slant height and value of π is constant = 3.14

Curved Surface Area of a Cone Formula

The curved surface area of a cone is the multiplication of pi, slant height, and the radius. In mathematics, the volume of a cone formula is given as –

\[\large Curved\;Surface\;Area\;of\;cone=\pi rs\]

Where,
r is the radius of cone.
h is the height of cone.
s is the slant height of the cone.

Where r is the radius, l is the slant height and value of π is constant = 3.14

Total Surface Area of a Cone Formula

The formula to compute the total surface area of a cone in mathematics is given as –

\[\large Total\;Surface\;Area\;of\;Right\;circular\;cone=\pi r(r+ \sqrt {h^{2}+r^{2}}) \]

Where,
r is the radius of cone.
h is the height of cone.

Where r is the radius, l is the slant height and value of π is constant = 3.14. to compute the slant height of cone, you can apply Pythagoras theorem, if you know the height and the radius.


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