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Big Ideas Math: Modeling Real Life, Grade 7

BI

Big Ideas Math: Modeling Real Life, Grade 7 View details

5. Volumes of Pyramids

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Exercise 12 Page 437

The volume of a pyramid is one third the area of its base times the height of the pyramid.

26 23yd^3

Practice makes perfect

Let's consider the given pyramid.

Triangular pyramid

We want to find the volume of the pyramid. Recall that the volume V of a pyramid is one third the area of the base B times the height of the pyramid h.

V=1/3 B h Let's use the diagram to identify the pyramid's height and write an expression for the area of its base. Remember that the area of a triangle is half the product of any base and its height.

Triangular pyramid

Now we can substitute 12* 5* 4 for B and 8 for h into the formula and calculate the volume of the pyramid.

V = 1/3Bh

B= 1/2 * 5* 4, h= 8

V = 1/3 ( 1/2 * 5* 4) (8)

AssociativePropMult

Associative Property of Multiplication

V = (1/3 * 1/2) (5* 4 * 8)

Multiply fractions

V = (1* 1/3* 2 ) (5* 4 * 8)

Multiply

V = (1/6 ) (160)

MoveRightFacToNumOne

1/b* a = a/b

V=160/6

a/b=.a /2./.b /2.

V=160÷ 2/6÷ 2

Calculate quotient

V=80/3

▼

Write fraction as a mixed number

Write as a sum

V=78+2/3

Write as a sum of fractions

V=78/3+2/3

Calculate quotient

V=26+2/3

Add terms

V= 26 23

The volume of the pyramid is 26 23 cubic yards.

Subchapter links

Try It p.434-435

Self-Assessment for Concept & Skills p.435

Self-Assessment for Problem Solving p.436

Review & Refresh p.437

Concept, Skills, & Problem Solving p.437-438