6th Grade Math Textbook, Fundamentals

 &KDSWHU

11-8

Key Concept

V Bh, where Barea of the base and hheight

Volume (V) of a Pyramid

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3

6 in.

4 in.

6 in.

6 in.

6 in.

4 in.

Remember:The height of a pyramid

is the perpendicular distance from the

pyramid’s base to its vertex.

pyramid

height  8 ft

3 ft 4 ft

Find the volume of each of the two figures above.

Volume of Pyramids

Objective To use formulas to find the volumes of pyramids• To find unknown

dimensions given the volumes of rectangular and triangular pyramids

Charmaine has two containers—one in the shape
of a square pyramid and the other in the shape
of a square prism. The bases of the containers
are congruent and their heights are equal. As an
experiment, she completely fills the pyramid with
water and empties it into the prism. How many
times does she have to do this in order to
completely fill the prism?

The volume of a pyramid is equal to the volume of

a prism if the figures have equal heights and congruent

bases. So to fill the prism with water, Charmaine has to

fill and empty the pyramid three times.

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Volume of pyramid:V Bh

V wh

 (6 • 6)4

 (36)4

(12)4  48

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Check:48 in.^3 (144 in.^3 )

48 in.^3 48 in.^3 Tr u e

The volume of the pyramid is 48 in.^3 , which is the volume of the prism.^13

?

^13

Volume of prism:Vwhor VBh

V(6)(6)(4)

(36)4

 144

The formula also applies to triangular pyramids.

Find the volume of the pyramid at the right.

V Bh Formula for the volume of a pyramid

 ( bhbase)hpyramid

 ( • 3 • 4) 8 Substitute known values.

 (6)8 Simplify within the parentheses.

(2)8  16 Multiply.

So the volume of the triangular pyramid is 16 ft^3.

Substitute the formula for the

area of a triangle for B.

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