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?

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 circular cone instead.

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 finite number of sides and hence, 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 vertex (similar to a pyramid).

The three main dimensions of a cone are: the radius, the height, and the slant height. The radius of a cone is measured from the center of the circular base to any point on its circumference and the slant height of a cone is measured from 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 volume of the cone, r is the radius of the circular base of the cone and h is the height of the cone

## 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 slant height of the cone

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

### 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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