9-5 volume of prisms and cylinders warm up warm up lesson presentation lesson presentation problem...

9-5 Volume of Prisms and Cylinders

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

9-5 Volume of Prisms and CylindersMath Journal (5 Min)

• “What Do I Know About” – Each student will be given the title of the lesson that will be taught that day. They must then, at the beginning of class, write about what they know about the lesson before they have been taught the lesson, and at the end of class, write about what they now know about the lesson after they have been taught the lesson. Then, each student will discuss his/her answers within their group. Finally, to leave class, each student will have to give/write 1 sentence that they now know that pertained to the lesson.

9-5 Volume of Prisms and CylindersHomework Review (5 Min)


Warm UpIdentify the figure described.

1. two triangular faces and the other faces in the shape of parallelograms

2. one hexagonal base and the other faces in the shape of triangles 3. one circular face and a curved lateral surface that forms a vertex

triangular prism

hexagonal pyramid

cone


Problem of the Day

How can you cut the rectangular prism into 8 pieces of equal volume by making only 3 straight cuts?

9-5 Volume of Prisms and CylindersTextbook Examples (I Do) (5 Min)


Learn to find the volume of prisms and cylinders.


Vocabulary

volume


Any three-dimensional figure can be filled completely with congruent cubes and parts of cubes. The volume of a three-dimensional figure is the number of cubes it can hold. Each cube represents a unit of measure called a cubic unit.


4 cm · 3 cm · 1cm = 12 cm3

length · width · height = volume

area ofbase

· height = volume

1 cm

4 cm

3 cm

To find the volume of a rectangular prism, you can count cubes or multiply the lengths of the edges.


Find the volume of the figure.

Additional Example 1A: Using a Formula to Find the Volume of a Prism

V = Bh

The volume of the prism is 192 ft3.

Use the formula.

The base is a square: B = 4 4 = 16.

V = 16 12 Substitute for B and h.

Multiply.V = 192



Additional Example 1B: Using a Formula to Find the Volume of a Prism

V = Bh

The volume of the triangular prism is 36 cm3.

Use the formula.

The base is a triangle: B = 1/2 3 4 = 6.


Multiply.V = 36



Check It Out: Example 1A

V = Bh

The volume of the prism is 72 in3.

Use the formula.

The base is a square: B = 3 3 = 9.


Multiply.V = 72



Check It Out: Example 1B

V = Bh

The volume of the triangular prism is 72 in3.

Use the formula.

The base is a triangle: B = 1/2 3 3 = 4.5.

V = 4.5 16 Substitute for B and h.

Multiply.V = 72


Any unit of measurement with an exponent of 3 is a cubic unit. For example, cm3 means “cubic centimeter” and in3 means “cubic inch.”

Reading Math


Finding the volume of a cylinder is similar to findingthe volume of a prism.


A can of tuna is shaped like a cylinder. Find its volume to the nearest tenth. Use 3.14 for .

Additional Example 2: Using a Formula to Find the Volume of a Cylinder

V = r2h

The radius of the cylinder is 5 m, andthe height is 4.2 m

V 3.14 · 52 · 4.2

V 329.7

The volume is about 329.7 m3.

Use the formula.

Substitute for r and h.

Multiply.


Check It Out: Example 2

V = r2h

The radius of the cylinder is 7 m, and the height is 3.8 m

V 3.14 · 72 · 3.8

V 584.668

The volume is about 584.7 m3.

Use the formula.

Substitute for r and h.

Multiply.

Find the volume of a cylinder to the nearest tenth. Use 3.14 for .

3.8 m7 m


Find the volume of the composite figure to the nearest ft. Use 3.14 for

Additional Example 3: Finding The Volume of a Composite Figure

Volume of a

composite figure

Volume of

prism = +

Volume of triangular

prism

V = + Bh Bh

V (4)(6)(12) + (½)(4)(6) · (6)

V 288 + 72

V 360 ft3


Find the volume of the composite figure to the nearest ft. Use 3.14 for

Check It Out: Example 3

Volume of a

composite figure

Volume of

prism = +

Volume of triangular

prism

V = + Bh Bh

V (4)(5)(10) + (½)(4)(5) · (6)

V 200 + 60

V 260 ft3

5 ft

10 ft

9-5 Volume of Prisms and CylindersClass work Problems (We Do) (10 Min)

• Pg. 384-385 (1-6)

9-5 Volume of Prisms and CylindersSmall Group CW(Yall Do) (10 Min)

• Pg. 384-385 (8-18 EOE)

9-5 Volume of Prisms and CylindersHomework (You Do) (10 Min)

• Pg. 384-385 (7, 11, 13, 15, 17 odd)

9-5 Volume of Prisms and CylindersMath Journal (5 Min)

• “What Do I Know About” – Each student will be given the title of the lesson that will be taught that day. They must then, at the beginning of class, write about what they know about the lesson before they have been taught the lesson, and at the end of class, write about what they now know about the lesson after they have been taught the lesson. Then, each student will discuss his/her answers within their group. Finally, to leave class, each student will have to give/write 1 sentence that they now know that pertained to the lesson.


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz

1. Find the volume of the prism.

4,069.4 cm3

2. A storage tank is shaped like a cylinder. Find its volume to the nearest tenth. Use 3.14 for

792 cm3

3. Find the volume of the composite figure.

216 in3


1. Identify the volume of the prism.

A. 35 cm3

B. 95 cm3

C. 133 cm3

D. 665 cm3



2. A piece of wood is shaped like a cylinder. Find its volume to the nearest tenth. Use 3.14 for

A. 5849.8 cm3

B. 1950 cm3

C. 414 cm3

D. 207 cm3


9-5 volume of prisms and cylinders warm up warm up lesson presentation lesson presentation problem...

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