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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Volumes of Prisms and Cylinders

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Exercise 28 Page 836

The volume of a rectangular prism is equal to the product of its dimensions.

225 cubic centimeters

Practice makes perfect

Let's analyze the given composite solid. We will assume that the bases are rectangles — otherwise, we have too little data to solve the exercise.

It consists of two solids.

A rectangular bottom prism with a length of l= 11 cm, a width of w= 3 cm, and a height of h= 5 cm.
A rectangular top prism with a length of l= 4 cm, a width of w= 3 cm, and a height of h=10-5= 5 cm.

The volume of a rectangular prism is equal to the product of its dimensions. Let's find the volumes of the two rectangular prisms.

Prism	Bottom	Top
Dimensions	l= 11, w= 3, h= 5	l= 4, w= 3, h= 5
Volume	V= l w h
Volume	V_\text{bottom}=({\color{#0000FF}{11}})({\color{#009600}{3}})({\color{#FF0000}{5}})=165	V_\text{top}=({\color{#0000FF}{4}})({\color{#009600}{3}})({\color{#FF0000}{5}})=60

The volume of the composite solid is the sum of the volumes of these two smaller rectangular prisms.

V_\text{solid}=V_\text{bottom}+V_\text{top}

V_\text{bottom}={\color{#0000FF}{\textcolor{darkorange}{165}}}, V_\text{top}={\color{#009600}{\textcolor{darkviolet}{60}}}

V_\text{solid}=\textcolor{darkorange}{165}+\textcolor{darkviolet}{60}

Add terms

V_\text{solid}=225

The volume of the composite solid is 225 cubic centimeters.

Subchapter links

Exercises p.834-838