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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 13 Page 437

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

80in.^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* 10* 6 for B and 8 for h into the formula and calculate the volume of the pyramid.

V = 1/3Bh

B= 1/2 * 10* 6, h= 8

V = 1/3 ( 1/2 * 10* 6) (8)

AssociativePropMult

Associative Property of Multiplication

V = (1/3 * 1/2) (10* 6 * 8)

Multiply fractions

V = (1* 1/3* 2 ) (10* 6 * 8)

Multiply

V = (1/6 ) (480)

MoveRightFacToNumOne

1/b* a = a/b

V=480/6

Calculate quotient

V= 80

The volume of the pyramid is 80 cubic inches.

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