Cone

CONE

CONE DEFINITION:

-a 3-dimensional solid objectthat 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 vertexthat is not aligned above the centre of the base.

Oblique Cone Right Cone

Vertex not aligned at the centreof 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