CONE
CONE DEFINITION:
-a 3-dimensional solid object that has :a) circular base,b) one vertex.
Vertex:a corner
For example, a triangle has 3 vertices.
How do we determine which is
a cone?
Has a circular
base
One vertex only
Volume of a cone
Example:Volume of a cone formula = 1/3 πr2H
π= 3.142r = 3 cm
H = 11 cm
Volume of a cone = 1/3 πr2H= 1/3 (3.142) (3)2 (11)
= 103.69 cm3
What if given slanted height but not height of cone?
Phythagoras Theorem
5cm
3cm
X cm
5cm
3cm
X cm
√( X2 + 32) = 52
X2 = 52 – 32
X2 = 16
X=√16
X= 4cm
Oblique Cone?
Definition :
-A cone with an vertex that is not aligned above the centre of the base.
Oblique Cone Right Cone
Vertex not aligned at the centre of the base
Vertex is not aligned at the centre of base
Height of vertex is in the center of the
circle
Formula
Volume of an oblique cone= 1/3 (area of base)(cone height)= 1/3 Bh
B= πr2
Formula of oblique cone = 1/3 Bh
B= πr2
π = 3.142r = 3 cmH = 9 cm
Volume of oblique cone= 1/3 Bh= 1/3 πr2h= 1/3 (3.142) (3)2(9)
= 84.83 cm3
Example:
Given radius of base is 3 cm, height of cone is 9 cm.
Calculate the volume of the oblique cone.
Conclusion
Volume of an oblique cone= 1/3 Bh
Volume of a right cone= 1/3πr2 H
B= Area of base
πr2 = Area of base
B = Area of base = πr2
Formula to find volume of oblique cone and right cone is the same.
A=πr2+πrL
Surface area of Cone
The End