The document discusses cones, frustums, and their properties. It defines a cone as having a circular base and curved side ending at an apex point. A frustum is formed from cutting off the tip of a cone with a cut perpendicular to the height, forming two parallel circular bases. The document provides formulas to calculate the volume and surface area of cones and frustums. It gives examples of applying the formulas to solve for volume and surface area.

1. CONE & FRUSTUM
GROUP MEMBERS :
TAN MIN CHUEN
CHANG HUEY YI
KAREN CHOO
EE HUI TENG
NG KWANG ZHOU
LEE YET YEE

2. 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.

3. 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.

4. TYPES AND PROPERTIES

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

6. TYPES AND PROPERTIES
FRUSTUM
Frustum 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.

7. VOLUME OF CONE
Definition : 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.

8. SURFACE AREA OF CONE
Formula
Curved surface area = πrs
Area of circle = πr2
Total surface area = πrs + πr2
r = radius
s =slant
Example :
Radius= 4cm
Slant= 5cm
Total surface area= (π x 4 x 5) + (π x 42)
= 113.1 cm2

9. 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

10. VOLUME OF FRUSTUM
H
(1)
(2)
Substitutin
g (1) in the
frustum
volume
formula
Substituting (2) in the frustum volume formula
r
R
r
h

11. VOLUME OF FRUSTUM
EXAMPLE:
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

12. 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
The surface area, not including the top
and bottom circles, is
A =
=

13. SURFACE AREA OF FRUSTUM
r = Radius of upper circular base
R = Radius of lower circular base
h = Height of the conical frustum