CONE & FRUSTUMGROUP MEMBERS :

TAN MIN CHUEN CHANG HUEY YI

KAREN CHOOEE HUI TENG

NG KWANG ZHOULEE YET YEE

WHAT IS CONE?

Oblique cone

A cone is a three-dimensional geometric shape. It consists of a base having the shape of a circle and a curved side (the lateral surface)

ending up in a tip called the apex or vertex.

Cones are divided into at least two categories :

Right circular cone

The angle between the lateral surface and the base is the same all around the cone. The apex is positioned right above the base’s

center point.

The angle between the lateral surface and the base is not the same all around the cone. The

apex is not positioned right above the base’s center point.

WHAT IS FRUSTUM?A frustum may be formed from a right circular cone by cutting off the tip of the cone with a cut perpendicular to the height, forming a lower base and

an upper base that are circular and parallel.

TYPES AND PROPERTIES

TYPES AND PROPERTIESCONE- A solid with a circular base and a curved side that ends in one point- It had one vertex.

TYPES AND PROPERTIESFRUSTUMFrustum of a right circular cone is that portion of right circular cone included between the base and a section parallel to the base not passing through the vertex

Properties of Frustum of Right Circular Cone

- The altitude of a right circular cone is the perpendicular distance

between the two bases. It is denoted by h.

- All element of a frustum of a right cone are equal. It denoted by L.

VOLUME OF CONEDefinition : The number of cubic units that will exactly fill a cone.

Volume of a cylinder = Therefore, volume of a cone = x area of base x height, where area of base =

Volume of a cone = , Where r= radius of the circular base of the cone, and

h= height of the cone

Volume of a cone is exactly one third the volume of a cylinder with the same

radius and height.

SURFACE AREA OF CONEFormulaCurved surface area = πrsArea of circle = πr2

Total surface area = πrs + πr2

r = radiuss =slant

Example :

Radius= 4cmSlant= 5cm

Total surface area= (π x 4 x 5) + (π x 42) = 113.1 cm2

VOLUME OF FRUSTUM

Volume of the entire cone

Volume of the tip cone

Volume of the frustum = Volume of entire cone – Volume of tip cone

VOLUME OF FRUSTUM

From similar triangles in the figure, we have

(1)

(2)

Substituting (1) in the frustum volume formula

Substituting (2) in the frustum volume formula

VOLUME OF FRUSTUMEXAMPLE:Find the volume of a frustum of a cone with bases of radii 5cm and 19cm. The height of this frustum is 6cm (π=3.14)Solution:Let h be the height, R the radius of the lower base, and r the radius of the upper base

== 3020.68 cm3

SURFACE AREA OF FRUSTUM

A conical frustum is created by slicing the top off a cone (with the cut made parallel to the base).

For a right circular cone, let  be the slant height and  and  the base and top radii. Then:

……1

SURFACE AREA OF FRUSTUM

The surface area, not including the top and bottom circles, is called lateral surface area

A =

=

SURFACE AREA OF FRUSTUM