9-6 volume of prisms warm up warm up lesson presentation lesson presentation problem of the day...

9-6 Volume of Prisms

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


Warm UpFind the area of each figure. Use 3.14 for .

96 in2

50.24 ft2

1. rectangle with base length 8 in. and height 12 in.

2. circle with diameter 8 ft


Problem of the Day

A rectangular park is bordered by a 3-foot-wide sidewalk. The park, including the sidewalk, measures 125 ft by 180 ft. What is the area of the park, not including the sidewalk?20,706 ft2

Volume of Prisms


MA.6.G.4.3 Determine the missing dimension of a prism…given its volume…or the volume given the dimensions.

Also MA.6.A.3.4

Sunshine State Standards


Vocabulary

volume


Volume is the number of cubic units needed to fill a space.


You need 10, or 5 · 2, centimeter cubes to cover the bottom layer of this rectangular prism.

You need 3 layers of 10 cubes each to fill the prism. It takes 30, or 5 · 2 · 3, cubes.

Volume is expressed in cubic units, so the volume of the prism is 5 cm · 2 cm · 3 cm = 30 cm3.


Additional Example 1: Finding the Volume of a Rectangular Prism

Find the volume of the rectangular prism.

V = lwh Write the formula.

V = 26 • 11 • 13 l = 26; w = 11; h = 13

Multiply.V = 3,718 in3


Check It Out: Example 1A

Find the volume of each rectangular prism.

V = lwh = 2 × 3 × 8 = 48 ft 3


Check It Out: Example 1B


V = lwh = 1 × 1 × 2 = 2 km3


Check It Out: Example 1C


V = lwh = 8.4 × 5.1 × 6 = 257.04 in 3


To find the volume of any prism, you can use the formula V= Bh, where B is the area of the base, and h is the prism’s height.


Additional Example 2: Finding the Volume of a Triangular Prism

Find the volume of thetriangular prism.

V = Bh Write the formula.

V = ( • 3.9 • 1.3) • 412__ B = • 3.9 • 1.3; h = 4.1

2__

Multiply.V = 10.14 m3


The bases of a prism are always two congruent, parallel polygons.

Caution!


Check It Out: Example 2A

V = Bh

(8)(7)12

= 336 ft

23

= 1


Check It Out: Example 2B

V = Bh

= ( )(2)121

21

43

= 87 m3

21

m


Check It Out: Example 2C

V = Bh

= (3)(5.4)8.621

= 69.66cm3


Additional Example 3: Problem Solving Application

Suppose a facial tissue company ships 16 cubic tissue boxes in each case. What are the possible dimensions for a case of tissue boxes?

11 Understand the ProblemThe answer will be all possible dimensions for a case of 16 cubic boxes.

List the important information:

• There are 16 tissue boxes in a case.

• The boxes are cubic, or square prisms.


You can make models using cubes to find the possible dimensions for a case of 16 tissue boxes.

22 Make a Plan

Additional Example 3 Continued


Solve33

You can make models using cubes to find the possible dimensions for a case of 16 cubes.


The possible dimensions for a case of 16 cubic tissue boxes are the following: 16 x 1 x 1, 8 x 2 x 1, 4 x 4 x 1, and 4 x 2 x 2.


Notice that each dimension is a factor of 16. Also, the product of the dimensions (length • width • height) is 16, showing that the volume of each case is 16 cubes.

Look Back44



Check It Out: Example 3A toy box is a rectangular prism that is 3 ft long, 2 feet wide, and 2 feet tall. Another toy box has the same dimensions, except that it is longer. If the longer toy box has a volume that is 50% greater than the original toy box, what is the length of the longer toy box?

The original volume is 3 × 2 × 2 = 12 ft . 50% of 12 is 6, so the longer toy box has a volume of 12 + 6 = 18 ft . So L × 2 × 2 = 18, and L = 18 ÷ 4 = 4.5. The length of the longer toy box is 4.5 feet.

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9-6 volume of prisms warm up warm up lesson presentation lesson presentation problem of the day...

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