__In this note, you will learn:__

· __What are cones?__

· __Volume and surface area of cones__

· __Application questions involving volume and surface area of cones __

__What is a cone?__

__What is a cone?__

Visually, a cone is similar to a pyramid. However, a cone does not constitute as a pyramid because ** a pyramid must have a polygonal base** as mentioned above and a cone has a

**instead.**

__circular cone__Of course, one might argue that a circle is essentially a ** polygon with an indefinite number of sides**, but a polygon is defined to have a

**number of sides and hence,**

__finite__**.**

__a circle is NOT a polygon__Based on geometrical terms, A cone is a three-dimensional geometric shape that thins out evenly from a flat base (typically circular) to a point called the ** apex** or

**(similar to a pyramid).**

__vertex__The ** three** main dimensions of a cone are: the

**, the**

__radius__**, and the**

__height__**. The radius of a cone is measured from**

__slant height__**and the slant height of a cone is measured from**

__the center of the circular base to any point on its circumference__**.**

__any point on the circumference of the circular base to the apex or vertex of the cone____How to find the volume of cone?__

The general formula to find the volume of a cone is:

**V = 1/3 **π r^2 h **OR V = 1/3 X Base Area X Height**

where ** V** is the

**of the cone,**

__volume__**is the**

__r__**of the circular base of the cone and**

__radius__**is the**

__h__**of the cone**

__height____How to find the surface area of cone?__

The general formula to find the total surface area of a cone is:

**Total Area = π r l + π r^2 **

where ** l** is the

**of the cone**

__slant height__Note: The slant height of a cone can be found by using ** Pythagoras’ Theorem**.

**OR**** **

### Total Area = Curved surface area of cone + surface area of circular base

__Application example of cones__

__Application example of cones__

__Finding the volume of a cone__

A cone has a circular base of radius 15 cm and a height of 27 cm. Find the volume of the cone.

Solution:

Volume of cone = **1/3 π r^2 h **

= 1/3 π (15)^2 (27)

= 6360 cm^3 (to 3 s.f.)

__Finding the total surface of a cone__

A cone has a circular base of radius 10 cm and a slant height of 19 cm. Find the total surface area of the cone.

Solution:

Total surface area of cone = **π r l + π r^2**

= π (10)(19) + π (10)^2

= 190π + 100π

= 290π

= 911 cm^2 (to 3 s.f.)

And that’s all for today, students! Math Lobby hopes that after this article, you have a clear understanding on cones, their formulae and its application!

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