surface areas of solids.notebooknreevesmath.weebly.com/uploads/1/4/2/8/14286293/...Lesson objectives...

surface areas of solids.notebook

1

September 06, 2013

Surface Areas of Solids

Lesson objectives Teachers' notes

6.1 Drawing 3-Dimensional Figures

Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. CC.7.G.3


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Answer a

Answer b


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Homework ws

Surface Area of Solids 1

Use the NECAP reference sheet for formulas


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Tap to reveal Tap to reveal

Tap to reveal Tap to reveal

Tap to reveal


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Answ

er 4Answ

er 5Answ

er 3

Homework ws


Use the NECAP reference sheet for formulas


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6.2 Surface Areas of Prisms


Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. CC.7.G.4

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. CC.7.G.6


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Tap to reveal

Tap to reveal

Homework:Ws. Surface Area of a Prism 1


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Write a formula.

or 126 in2.


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Homework:Ws. Surface Area of a Prism 2


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6.2b Circles


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Check Point

18 in.

12 in. or .5 ft.

Answer the following questions.(Erase to reveal the answer.)


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6.3 Surface Areas of Cylinders


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Answ

er aAnsw

er b


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6.4 Surface Areas of Pyramids


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Answ

er aAnsw

er b

Answ

er dAnsw

er c


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Answ

er aAnsw

er bAnsw

er c

Answ

er b


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Check Point

Homework:Worksheet Surface Area of Pyramids 1


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207 cm2erase


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Check Point

1) What is the surface area of the pyramid at the right?

2) WHAT IF? In Example 3, one bundle of shingles covers 32 square feet. How many bundles should you buy to cover the roof ?

17 bundles

105.6 ft2




6.5 Surface Areas of Cones


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2.5 in.

3 in.≈ 43.2 in.2

2 in. 1.5 in.

3 in.≈ 31.4 in.2

3 in. 3 in. 3 in.

1 in. 0.5 in.

≈ 21.2 in.2 ≈ 12.6 in.2 ≈ 5.5 in.2

erase to reveal.

The surface area of the cone is about 5.5 square inches. The radius of the base decreases by 0.5 inch each time one part of the circle is removed. The slant height remains the same because the radius of the original circle remains the same. The surface area of the cone decreases each time one part of the circle is removed.

Describe the pattern.

Check Point

IN YOUR OWN WORDS How can you find the surface area of a cone? Draw a diagram with your explanation.

To find the surface area of a cone, find the sum of the area of the base, which is π r2 , and the area of the lateral surface.

Diagram

Tap to reveal.


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Check Point


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Check Point


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6.6 Surface Areas of Composite Solids

The four solids are a square pyramid, a cone, a squareprism, and a cylinder.

Sample answer: To find the surface area of the model,use a net to find the surface area of each of the foursolids. A net will allow you to accurately label thedimensions of the solids, which will help to find thesurface area.


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For each 1 unit increase of n, the increase in the surface area is two square units greater than the last increase. A figure that has a base of 10 blocks, 10 blocks in the top view, and 10 blocks in the front view. Since the sum from 1 to 10 is 55, there are 55 blocks in the side view.

The surface area of a figure with a base of 10 blocks is 150 square units.

Sample answer: The flat roof has the smallest area, so it would be the cheapest to build. The cross-hipped roof would be the most expensive because it has a very large surface area and there would be a lot of wasted shingles.


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Check Point

Identify the solids that make up the composite solid. Then find the surface area. Round your answer to the nearest tenth.

1) 2)

Attachments

Surface Area of Solids 1 answers.pdf

Surface Area of Solids 1.pdf

Surface Area of Solids 2 answers.pdf

Surface Area of Solids 2.pdf

MathRefSheetGR7.pdf

Surface Area of Prisms 1 answer.pdf

Surface Area of Prisms 1.pdf

Surface Area of Prisms 2 answer.pdf

Surface Area of Prisms 2.pdf

Circles answers.pdf

Circles.pdf

Surface Area of Cylinders 1 key.pdf

Surface Area of Cylinders 1.pdf

Surface Area of Cylinders 2 key.pdf

Surface Area of Cylinders 2.pdf

Surface Area of Composite Solids 1 key.pdf

Surface Area of Composite Solids 1.pdf

Surface Area of Composite Solids 2 key.pdf

Surface Area of Composite Solids 2.pdf


8 Math

2013-2014

Draw the front, side, and top views of the stack of cubes. Then find the surface area

and volume.

1. 2. 3.

4. 5. 6.

Name ___Answer___________

Date _____________________

Class ____________________

SMART Notebook

x x x


8 Math

2013-2014

Draw the front, side, and top views of the stack of cubes. Then find the surface area

and volume.

1. 2. 3.

4. 5. 6.

Name ____________________

Date _____________________

Class ____________________

SMART Notebook


8 Math

2013-2014

1) VOCABULARY Compare and contrast prisms and cylinders.

Prisms and cylinders both have two parallel, identical bases. The bases of a cylinder are

circles. The bases of a prism are polygons. A prism has lateral faces that are

parallelograms or rectangles. A cylinder has one smooth, round lateral surface.

2) VOCABULARY Compare and contrast pyramids and cones.

Pyramids and cones both have one base and one vertex not at the base. The base of a

cone is a circle. The base of a pyramid is a polygon. A pyramid has lateral faces that are

triangles. A cone has one smooth lateral surface.

3) WRITING Give examples of prisms, pyramids, cylinders, and cones in real life.

Sample answers: Prisms: A cereal box is a rectangular prism. A pup tent with parallel triangular bases at

the front and back is a triangular prism.

Pyramids: The Egyptian pyramids are rectangular pyramids. The roof of a house forms a

pyramid if it has lateral faces that are triangles meeting at a common vertex.

Cylinders: Some examples of cylinders include a soup can, a tuna fish can, and an

unsharpened round pencil. Cones: Some examples of cones include a traffic cone, an ice

cream cone, a party hat, and the end of a sharpened pencil.

Identify the shape of the base. Then name the solid.

4)

The base is a hexagon,

so the solid is a

hexagonal

pyramid.

5) The bases are circles, so

the solid is a cylinder.

6)

The bases are pentagons,

so the solid is a

pentagonal

prism.

Draw the solid.

7) Triangular prism

8) Pentagonal prism

Name ___KEY_____________

Date _____________________

Class ____________________

9) Rectangular pyramid

10) Hexagonal pyramid

11) Cone

12) Cylinder

Draw the front, side, and top views of the solid.

13)

14)

15)

16)

SMART Notebook


8 Math

2013-2014

1) VOCABULARY Compare and contrast prisms and cylinders.

2) VOCABULARY Compare and contrast pyramids and cones.

3) WRITING Give examples of prisms, pyramids, cylinders, and cones in real life.

Identify the shape of the base. Then name the solid.

4)

5)

6)

Draw the solid.

7) Triangular prism 8) Pentagonal prism

Name ____________________

Date _____________________

Class ____________________

9) Rectangular pyramid

10) Hexagonal pyramid

11) Cone

12) Cylinder

Draw the front, side, and top views of the solid.

13)

14)

15)

16)

SMART Notebook

New England Common Assessment ProgramMathematics Reference Sheet – Grade 7

Rectangle Rectangular Prism

Trapezoid

Parallelogram

Triangle

Circle

b1

h

b2

l

w

B

h

h

b

h

b

lwArea =

bhArea =

Volume = area of the base • height

h(b1+b2)Area =1—2

circumference = 2πr

π ≈ 3.14

bh1—2Area =

Bh=

Use the information below as needed to answer questions on the mathematics test.

The median of a data set isthe middle value or averageof the two middle valueswhen the values are arrangedin numerical order.

Median:

The mode of a data set is thevalue that occurs most often.

Mode:

Mean: The mean of a data set is thesum of all the values dividedby the number of values.

r

SMART Notebook

Surface Area of Prisms 1

8 Math

2013-2014

Draw a net for the prism. Then find the surface area.

1)

2)

3) 25 units

4) 48 units

5)

54 units


Date _____________________

Class ____________________

SMART Notebook


8 Math

2013-2014

Draw a net for the prism. Then find the surface area.

1)

2)

3)

4)

5)

Name ____________________

Date _____________________

Class ____________________

SMART Notebook


8 Math

2013-2014

1) OPEN-ENDED Describe a real-world situation in which you would want to find the

surface area of a prism.

Sample answer: You want to paint a large toy chest in the form of a rectangular prism, and in

order to know how much paint to buy, you need to know the surface area.

Find the indicated area for the rectangular

prism.

2) Area of Face A

3) Area of Face B

4) Area of Face C

5) Surface area of the prism

Find the surface area of the prism.

6)

7)

8)

9) GIFT BOX What is the least amount of wrapping paper needed to wrap a gift box that measures 8 inches by 8 inches by 10 inches? Explain.

448 in.2; The surface area of the box is 448 square inches, so that is the least

amount of paper needed to cover the box.


Date _____________________

Class ____________________

SMART Notebook


8 Math

2013-2014

1) OPEN-ENDED Describe a real-world situation in which you would want to find

the surface area of a prism.

Find the indicated area for the rectangular

prism.

2) Area of Face A

3) Area of Face B

4) Area of Face C

5) Surface area of the prism

Find the surface area of the prism.

6)

7)

8)

9) GIFT BOX What is the least amount of wrapping paper needed to wrap a gift box that measures 8 inches by 8 inches by 10 inches? Explain.

Name ____________________

Date _____________________

Class ____________________

SMART Notebook

Circles

8 Math

2013-2014

Find the circumference of each circle to the nearest tenth of a unit. Use 3.14 for π .

1) circle with diameter 4 cm.

12.6 cm

2) circle with radius 4 in.

25.1 in.

3) circle with radius 5.5 ft 34.5 ft

4) circle with diameter 3 m 9.4 m

5) Tire: The diameter of a bicycle tire is 26 inches. a. Find the circumference of the tire.

About 81.64 in.

b. How many rotations does the tire make to travel 95 feet? Explain your reasoning.

About 14 rotations

Name ____KEY____________

Date _____________________

Class ____________________

SMART Notebook

Circles

8 Math

2013-2014

Find the circumference of each circle to the nearest tenth of a unit. Use 3.14 for π .

1) circle with diameter 4 cm.

2) circle with radius 4 in.

3) circle with radius 5.5 ft

4) circle with diameter 3 m

5) Tire: The diameter of a bicycle tire is 26 inches. a. Find the circumference of the tire.

b. How many rotations does the tire make to travel 95 feet? Explain your reasoning.

Name ____________________

Date _____________________

Class ____________________

SMART Notebook

Surface Area of Cylinders 1

8 Math

2013-2014

Make a net for the cylinder. Then find the surface area of the cylinder.

Round your answer to the nearest tenth.

Name ___KEY_____________

Date _____________________

Class ____________________

SMART Notebook


8 Math

2013-2014

Make a net for the cylinder. Then find the surface area of the cylinder.

Round your answer to the nearest tenth.

Name ____________________

Date _____________________

Class ____________________

SMART Notebook


8 Math

2013-2014

1) CRITICAL THINKING Which part of the formula S = 2πr 2 + 2πrh represents the lateral surface area of a cylinder?

Because the lateral surface area is the product of the circumference of the

base and the height of the cylinder, it is represented by 2π rh.

2) CRITICAL THINKING Given the height and the circumference of

the base of a cylinder, describe how to find the surface area of the

entire cylinder.

To find the surface area of the entire cylinder, substitute the value of C into C = 2π r and solve for r. Then use the formula for the surface area of cylinder.

Find the surface area of the cylinder. Round your answer to the

nearest tenth.

3)

4)

Find the lateral surface area of the cylinder. Round your answer to the

nearest tenth.

5)

6)

Name ___KEY_____________

Date _____________________

Class ____________________

7) TANKER The truck’s tank is a stainless steel cylinder. Find the

surface area of the tank.

The surface area of the tank is about 1356.48 square feet.

8) ERROR ANALYSIS Describe and

correct the error in finding the surface

area of the cylinder.

The error is that only the lateral surface area is found. The areas of the

bases should be added.

SMART Notebook


8 Math

2013-2014

1) CRITICAL THINKING Which part of the formula S = 2πr 2 + 2πrh represents the lateral surface area of a cylinder?

2) CRITICAL THINKING Given the height and the circumference of

the base of a cylinder, describe how to find the surface area of the

entire cylinder.

Find the surface area of the cylinder. Round your answer to the

nearest tenth.

3)

4)

Find the lateral surface area of the cylinder. Round your answer to the

nearest tenth.

5)

6)

Name ____________________

Date _____________________

Class ____________________

7) TANKER The truck’s tank is a

stainless steel cylinder. Find the

surface area of the tank.

8) ERROR ANALYSIS Describe and

correct the error in finding the surface

area of the cylinder.

SMART Notebook

Surface Area of Composite Solids 1

8 Math

2013-2014

Identify the solids that form the composite solid. Then find the surface area. Round

your answer to the nearest tenth.

1)

cylinder and cone

2) square prism and square pyramid;

Find the area. (Skills Review Handbook)

3)

4)

5)

6) MULTIPLE CHOICE A cliff swallow nest is 86 meters above a canyon floor.

The elevation of the nest is −56 meters. What is the elevation of the canyon floor?

Name ___Key______________

Date _____________________

Class ____________________

SMART Notebook


8 Math

2013-2014

Identify the solids that form the composite solid. Then find the surface area. Round

your answer to the nearest tenth.

1)

2)

Find the area. (Skills Review Handbook)

3)

4)

5)

6) MULTIPLE CHOICE A cliff swallow nest is 86 meters above a canyon floor.

The elevation of the nest is −56 meters. What is the elevation of the canyon floor?

Name ____________________

Date _____________________

Class ____________________

SMART Notebook


8 Math

2013-2014

1) OPEN-ENDED Draw a composite solid formed by a triangular prism and a cone.

2) REASONING Explain how to find the surface area of the

composite solid.

To find the surface area of the composite solid, first find the surface area of the cone, but

do not include the base. Then find the surface area of the cylinder and subtract the area

of the base of the cone. The surface area of the solid is the sum of the surface areas of the

cone and the cylinder.

Find the surface area. Round your answer to the nearest tenth.

3)

33.0 in.2

4)

245 m2

REASONING Find the surface area of the solid. Round your answer to the nearest

tenth.

5)

Name ____________________

Date _____________________

Class ____________________

The surface area of the figure can be found by calculating the surface area of the large

rectangular prism, subtracting the top and bottom of the small rectangular prism, then

adding the sides of the small prism. Surface

area of the large rectangular prism:

SMART Notebook


8 Math

2013-2014

1) OPEN-ENDED Draw a composite solid formed by a triangular prism and a cone.

2) REASONING Explain how to find the surface area of the

composite solid.

Find the surface area. Round your answer to the nearest tenth.

3)

4)

REASONING Find the surface area of the solid. Round your answer to the nearest

tenth.

5)

Name ____________________

Date _____________________

Class ____________________

SMART Notebook

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surface areas of solids.notebooknreevesmath.weebly.com/uploads/1/4/2/8/14286293/...Lesson objectives...

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