math slide ok-11860
TRANSCRIPT
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 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 FRUSTUMVolume of the entire cone
Volume of the tip cone
Volume of the frustum = Volume of entire cone – Volume of tip cone
VOLUME OF FRUSTUMH
(1)
(2)
Substituting (1) in the frustum volume formula
Substituting (2) in the frustum volume formula
r
Rr
h
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
The surface area, not including the top and bottom circles, is
A = =