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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

Chapter Test

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Exercise 4 Page 661

Find the volume of the prism-shaped sections and the volume of the pyramid-shaped section separately.

280/3≈ 93.3 ft^3.

Practice makes perfect

We want to find the volume of a composite solid in the shape of an prism with a pyramid attached at its top.

Prism with a pyramid attached on top

We will first find the volume of the prism and then the volume of the pyramid. We will then add the results to find the volume of the solid. Let's do it!

Volume of the Prism

Let's begin by finding the volume of the prism.

Prism with a pyramid attached on top. Prism highlighted

The volume of a prism is the product of the area of the base and the prism's height. V=Bh Our prism has a rectangular base, B, and its area is the product of the length and the width. V=Bh ⇒ V = l wh Let's substitute the corresponding values in the formula and find its volume.

V = l wh

SubstituteValues

Substitute values

V = 5( 2)( 8)

Multiply

V = 80

The prism has a volume of 80ft^3.

Volume of the Pyramid

The top section of the solid is in the shape of a pyramid.

Prism with a pyramid attached on top. Pyramid highlighted

The volume of a pyramid is one third times the product of the area of the base and the pyramid's height. The base is a rectangle and its area is the product of its length and its width. V=1/3Bh ⇒ V=1/3l wh Let's substitute the dimensions of the pyramid into the formula to find its volume.

V=1/3l wh

SubstituteValues

Substitute values

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

▼

Simplify right-hand side

Multiply

V = 1/3(40)

MoveLeftFacToNumOne

a* 1/b= a/b

V = 40/3

Volume of the Solid

To find the volume of the composite solid we will use the Volume Addition Postulate.

The volume of a solid is the sum of the volumes of all its non-overlapping parts.

The solid has two non-overlapping parts, a prism and a pyramid. Let's add their volumes. V_(solid)= V_(prism)+ V_(pyramid) ⇓ V_(solid)= 80+ 40/3= 280/3≈ 93.3 The solid has a volume of 2803≈ 93.3 ft^3.

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Exercises p.661