cone is a pyramid, usually with a circular base, which tapers to a point at the top, called the vertex or apex.

e.g.

Y9_Cones_01.gif

If the vertex is directly above the centre of the base, the cone is called a right cone.

There are three key measurements for a cone.

The radius, r
The height , h
The slant height, l

Volume of a Cone

The volume of a cone uses the formula for the volume of a pyramid

Y9_Cones_02.gif

V = 13 × (area of base) × h

=13πr2

Surface Area of a Cone

The surface area of a cone is the sum of the area of the base and the area of the curved surface of the cone.

S = π r l + π r 2

= π r (l + r)

Y9_Cones_04.gif

Examples of Cone Calculations

Examples
Calculation

 

Y9_Cones_05.gif

Find the volume, use π = 3.1

V = 13πr2h

V = 13 × 3.1 × 52 × 12

V = 310 cm3

For the cone shown above, find the surface area.

Surface area

= πr2 + πrl

= 3.1 × 52 + 3.1 × 5 × 13

= 77.5 + 201.5

= 279 cm2