VOLUME of PYRAMIDS Consider a pyramid and a prism having equal heights and bases with equal areas. If the pyramid is filled with sand and its contents.

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Presentation transcript:

Volume of Rectangular Pyramids EQ: How do you find the volume of a rectangular Pyramid ?

VOLUME of PYRAMIDS Consider a pyramid and a prism having equal heights and bases with equal areas. If the pyramid is filled with sand and its contents poured into a prism, only one- third of the prism will be filled. Thus the volume of a pyramid is ⅓ the volume of the prism. w = 4 cm l = 9 cm h = 6 cm base

The volume of a pyramid is related to the volume of a prism with the same base and height. The relationship can be verified by dividing a cube into three congruent square pyramids, as shown.

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Formula

Pyramids are classified according to their base. Rectangular Pyramid- the base is a rectangle. Triangular Pyramid- the base is a triangle.

EXAMPLE 1: FIND THE VOLUME OF A RECTANGULAR PYRAMID Solution: V = ⅓(bh)h V = ⅓(8 x7)(6 ) V = ⅓ x 56 x 6 V = ⅓ x 336 V = 112 in3

EXAMPLE 2: FIND THE VOLUME OF A RECTANGULAR PYRAMID Solution: V = ⅓Bh = ⅓(4 x 10) x 6 = ⅓ (240 cm³) V = 80 cm³

Volume of Triangular Pyramids EQ: How do you find the volume of a Triangular Pyramid ?

Example 1

Example 2 3