Vertex

Lateral face

Polygonal base

Height of the pyramid

The lateral faces are congruent isosceles triangles.

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Base is a Triangle Base is a SquareTriangular Pyramid Square Pyramid

PyramidsPyramidsA pyramid is named after the shape of its base.A pyramid is named after the shape of its base.

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Relationship between the volume of a pyramid and the volume of a prism with the same base area and height.

You need 3 times to fill up the volume of the pyramid.Volume of pyramid = the volume of the prism

= base area height

31

Prism

Pyramid With sameBase area & height

Cones

Curved surface(Lateral surface)Base

radius

Vertex

HeightSlant height

A cone is very much like a pyramid.

Instead of a polygon, it has a circle as its base.It also has a single curved surface, instead of a set of flat triangular faces.

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Volume of a Cone

We observe that the contents of three cones will exactly fill one cylinder.

Volume of a cone = volume of cylinder= area of base height

= r2h

31

31

31 r is the radius

h is the height

• Volume of a Pyramid

BhV31

Volume HeightBase Area

B

• Volume of a Cone

BhV31

Volume HeightBase Area

rB

Egyptian Pyramid

The ConeA Cone is a three dimensional solid with a circular base and a curved surface that gradually

narrows to a vertex.

Volume of a Cone=

+ + =

Find the volume of a cylinder with a radius r=1 m and height h=2 m. Find the volume of a cone with a radius r=1 m and height

h=1 m

Volume of a Cylinder = base x height = r2h

= 3.14(1)2(2)

= 6.28 m3

Exercise1

Volume of a Cone = (1/3) r2h

= (1/3)(3.14)(1)2(2)

= 2.09 m3