Digits, Grade 7, Volume 1, Homework Helper

Part 3

Example Finding Volumes of Hexagonal Prisms

Ms. Adventure's Japanese box has the shape of a regular hexagonal prism. To the nearest cubic inch what is the amount of space inside the box?

A regular hexagonal prism of height 4 in. The top and bottom bases have sides of length 3 in. The distance from the center of the base and perpendicular to a side is 2.6 in.

Solution

Use V = Bh to find the volume of the prism.

Step 1 Find the area of the hexagonal base.

A hexagon formed from six equilateral triangles with side length 3 in. and height 2.6 in.

table with 5 rows and 3 columns , row1 column 1 , table with 2 rows and 1 column , row1 column 1 , cap theareaofthebaseis . 6 . timesthe , row2 column 1 , areaofonetriangle. , end table , column 2 b , column 3 equals 6 middle dot . areaofonetriangle , row2 column 1 , table with 2 rows and 1 column , row1 column 1 , cap usetheformulafortheareaofa , row2 column 1 , triangle. , end table , column 2 , column 3 equals 6 middle dot , 1 half , bh , row3 column 1 , table with 3 rows and 1 column , row1 column 1 , cap substitute . 3 . forthebaseofthe , row2 column 1 , triangle . bold b comma , bold ehnd , 2.6 . fortheheight , row3 column 1 , ofthetriangle . bold h . , end table , column 2 , column 3 equals 6 middle dot , 1 half , open 3 close open 2.6 close , row4 column 1 , table with 2 rows and 1 column , row1 column 1 , cap multiplytofindtheareaofthe , row2 column 1 , triangle , . , end table , column 2 , column 3 equals 6 middle dot 3.9 , row5 column 1 , cap simplify. , column 2 , column 3 equals , 23.4 , end table

Step 2 Find the volume of the prism.

table with 3 rows and 2 columns , row1 column 1 , table with 2 rows and 1 column , row1 column 1 , cap usetheformulaforthevolumeofa , row2 column 1 , prism. , end table , column 2 v equals cap bh , row2 column 1 , table with 2 rows and 1 column , row1 column 1 , cap substitute . 23.4 . fortheareaofthebase , row2 column 1 , b comma , and , 4 . fortheheightoftheprism . bold h . , end table , column 2 equals open , 23.4 , close open 4 close , row3 column 1 , cap multiply. , column 2 equals , 93.6 , end table

The volume of the box is about 94 in3.


End ofPage 183

Table of Contents

Digits, Grade 7, Volume 1, Homework Helper Unit A: Number and Operations Unit B: Expressions, Equations, and Relationships Unit C: Measurement and Geometry Unit D: Proportionality English/Spanish Glossary Formulas Math Symbols Formulas Measures Properties