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[PDF] Find the volume of each prism 1 SOLUTION: The volume V of a

The volume V of a prism is V = Bh, where B is the 3 the oblique rectangular prism shown The planter is to be filled inches below the top, so Find each measure to the nearest tenth the base area and height of each triangular prism

[PDF] Find the volume of each prism 1 SOLUTION: The volume V of a

SOLUTION: The volume V of a prism is V = Bh, where B is the 3 the oblique rectangular prism shown SOLUTION: inches below the top? Find each measure to the nearest tenth 30 the base area and height of each triangular prism

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2 Find the volume of the composite space figure to the nearest whole number The right prism below has bases which are equilateral triangles of side length 4 to the nearest tenth, if necessary Rect Prism + Triangular Prism V=41004)

[PDF] Surface area and volume

Questions 1 to 3 refer to the prism below 4 Calculate the surface area of each of the following triangular prisms 2 Find the surface areas of these closed cylinders to the nearest whole number The volume of a right prism (or cylinder) is given by: V = A × h where A is the area of the base (or cross-sectional area) and h 

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The volume of a three-dimensional figure is the amount of space it round to the nearest whole number V = 56 ft3 12 7 yd w 9 yd V = 189 yd3 13 Find the volume of a rectangular prism with length 9 meters, width To find a missing dimension in a triangular prism, you will solve one or two equations shown below

[PDF] Surface Area and Volume

or your volume is increasing more?” Find the surface area of the solid shown by the net Finding the Surface Area of a Triangular Prism 2 nearest tenth Words The volume V of a prism is the product of the area of the base and the nearest whole number A rectangular prism and its dimensions are shown below

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Volume of the cylinder: V = Bh Sometimes the height of a triangular base in a triangular prism is not given Find the volume of each triangular prism to the nearest tenth 10 Find the volume of each composite figure to the nearest whole number From the figures shown below, choose the pyramid with volume closest

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Radius = + (diameter) Volume of prisms and cylinder: V = Bh Pyramid: SA = (# of triangular or lateral faces) ( bh )+ area of the base a 1) Find the area of the following figure 5m A=bh Round to the nearest tenth d=13 card 6) A) Find the volume of the pyramid below B) Find the surface area of the following V=Bh H

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V = Bh Finding Volume Work with a partner Consider a stack of square How can you find the volume of a prism or cylinder that is not a right prism volume The prisms below have equal heights h and equal cross-sectional Density is the amount of matter that an object has in a given unit of volume nearest gram

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a) Show that the volume of the box, V 3 cm , is given by 3 2 4 176 1536 V d) Find the maximum value for V , fully justifying the fact that it is the maximum 12 The figure above shows a solid triangular prism with a total surface area of 3600 2 this maximum value of V , correct to the nearest 3 where k is an integer

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Surface Area

and Volume

9.1 Surface Areas of Prisms9.1 Surface Areas of Prisms

9.2 Surface Areas of Pyramids9.2 Surface Areas of Pyramids

9.3 Surface Areas of Cylinders9.3 Surface Areas of Cylinders

9.4 Volumes of Prisms9.4 Volumes of Prisms

9.5 Volumes of Pyramids9.5 Volumes of PyramidsTake a deep breath and hold it.Ž Now, do you feel like your surface area

or your volume is increasing more?ŽI was thinking that I want the Pagodal roof instead of the Swiss chalet roof for my new doghouse.ŽBecause PAGODAL rearranges to spell 9

Example 1 Find the area of the rectangle.

7 mm3 mm

Area Yw Write formula for area.

7(3) Substitute 7 forYand 3 for w. 21 Multiply.
The area of the rectangle is 21 square millimeters.

Find the area of the square or rectangle.

1.

11 m9 m

2.

4.2 ft

8.5 ft

3. in. 2 3 in. 2 3 (6.G.1)

Example 2 Find the area of the triangle.

A 1 2 bhWrite formula. 1 2 (6)(7) Substitute 6 for b and 7 for h. 1 2 (42) Multiply 6 and 7. 21 Multiply
1 2 and 42.

The area of the triangle is 21 square inches.

Find the area of the triangle.

4. 5.

14 m 20 m 6.

What You

Learned Before

Descartes, how would you like it if I could

double the height of your cat food can?Ž

6 in.7 in.

15 cm30 cm

13 ft6 ft

354 Chapter 9 Surface Area and Volume

Surface Areas of Prisms9.1

How can you Þ nd the surface area of a prism?

Work with a partner. Copy the net for a rectangular prism. Label each side as h, w, or Y. Then use your drawing to write a formula for the surface area of a rectangular prism. h w

ACTIVITY: Surface Area of a Rectangular Prism

11

COMMON C

ORE

Geometry

In this lesson, you will

use two-dimensional nets to represent three-dimensional solids. Þ nd surface areas of rectangular and triangular prisms. solve real-life problems.

Learning Standard

7.G.6

Work with a partner.

a. Find the surface area of the solid shown by the net. Copy the net, cut it out, and fold it to form a solid. Identify the solid. 4 53
4 4 3 3 3 b. Which of the surfaces of the solid are bases? Why?

ACTIVITY: Surface Area of a Triangular Prism

22

Section 9.1 Surface Areas of Prisms 355

Work with a partner.

Use 24 one-inch cubes to form a rectangular prism that has the given dimensions. Draw each prism. Find the surface area of each prism. a. 4 = 3 = 2 Drawing Surface Area in. 2 b. 1 = 1 = 24 c. 1 = 2 = 12 d. 1 = 3 = 8 e. 1 = 4 = 6 f. 2 = 2 = 6 g. 2 = 4 = 3

ACTIVITY: Forming Rectangular Prisms

33
Use what you learned about the surface areas of rectangular prisms to complete Exercises 4 - 6 on page 359.

4. Use your formula from Activity 1 to verify your results in Activity 3.

5. IN YOUR OWN WORDS How can you nd the surface area of a prism?

6. REASONING When comparing ice blocks with the same volume, the ice

with the greater surface area will melt faster. Which will melt faster, the bigger block or the three smaller blocks? Explain your reasoning.

1 ft3 ft

1 ft 1 ft 1 ft 1 ft ism iPrismsms

Construct

Arguments

What method did

you use to Þ nd the surface area of the rectangular prism?

Explain.

Math Practice

356 Chapter 9 Surface Area and Volume

Lesson9.1

Surface Area of a Rectangular Prism

Words The surface area S of a rectangular prism is the sum of the areas of the bases and the lateral faces. h w base base lateral facelateral facelateral facelateral facew w w h

Algebra S + 2Yw - 2Yh - 2wh

EXAMPLEFinding the Surface Area of a Rectangular Prism 11

Find the surface area of the prism.

Draw a net.

S +

2Yw - 2Yh - 2wh

+ 2(3)(5) - 2(3)(6) - 2(5)(6) + 30 - 36 - 60 + 126

The surface area is 126 square inches.

Find the surface area of the prism.

1. 3 ft

2 ft4 ft

2. 5 m 8 m 8 m

Areas of

basesAreas of lateral faces

Exercises 7Ð9

Lesson Tutorials

Key Vocabulary

lateral surface area, p. 358 6 in. 3 in. 5 in.

5 in.3 in.6 in.

3 in.

5 in.5 in.

Section 9.1 Surface Areas of Prisms 357

Surface Area of a Prism

The surface area S of any prism is the sum of the areas of the bases and the lateral faces.

S + areas of bases - areas of lateral faces

EXAMPLEFinding the Surface Area of a Triangular Prism 22

Find the surface area of the prism.

Draw a net.

4 m3 m

5 m4 m

6 m3 m

Add the areas of the bases and the lateral faces.

S + areas of bases - areas of lateral faces

6 - 6 - 18 - 30 - 24

+ 84

The surface area is 84 square meters.

Find the surface area of the prism.

3.

12 m5 m

13 m 3 m 4.

3 cm4 cm5 cm

4 cm

Areas of Lateral Faces

Green lateral face:

3

6 + 18

Purple lateral face: 5

6 + 30

Blue lateral face: 4

6 + 24

Area of a Base

Red base:

1 2 3 4 + 6

5 m6 m

4 m 3 m

Remember

The area A of a triangle

with base b and height h is A + 1 2 bh.

Exercises 10Ð12

There are two identical

bases. Count the area twice.

358 Chapter 9 Surface Area and Volume

EXAMPLEReal-Life Application

44

The outsides of purple traps are coated with glue

to catch emerald ash borers. You make your own trap in the shape of a rectangular prism with an open top and bottom. What is the surface area that you need to coat with glue?

Find the lateral surface area.

S +

2Yh - 2wh

+ 2(12)(20) - 2(10)(20) Substitute. + 480 - 400 Multiply. + 880 Add.

So, you need to coat 880 square inches with glue.

5. Which prism has the greater

surface area?

6. WHAT IF? In Example 4, both

the length and the width of your trap are 12 inches. What is the surface area that you need to coat with glue?

Remember

A cube has 6 congruent

square faces. When all the edges of a rectangular prism have the same length s, the rectangular prism is a cube. The formula for the surface area of a cube is

S + 6s

2 . Formula for surface area of a cube

EXAMPLEFinding the Surface Area of a Cube

33

Find the surface area of the cube.

S + 6 s 2

Write formula for surface area of a cube.

+ 6(12) 2

Substitute 12 for s.

+ 864 Simplify. The surface area of the cube is 864 square meters. sss 12 m 12 m 12 m y.y.

12 in.10 in.20 in.

5 cm7 cm

15 cm

9 cm9 cm9 cm

Do not include the areas of

the bases in the formula. The lateral surface area of a prism is the sum of the areas of the lateral faces.

Exercises 13Ð15

Section 9.1 Surface Areas of Prisms 359

9+(-6)=3

3+(-3)=

4+(-9)=

9+(-1)=

Use one-inch cubes to form a rectangular prism that has the given dimensions.

Then Þ nd the surface area of the prism.

4. 1 = 2 = 3 5. 3 = 4 = 1 6. 2 = 3 = 2

Find the surface area of the prism.

7. 3 m 6 m 16 m 8. 7 mm 4 mm 5 mm 9.

5 yd3 yd

yd1 1 5 10.

15 ft17 ft

8 ft 20 ft 11. 5 m 5 m 7 m 6 m 4 m 12.

9 in.13.5 in.

10 in.

9 in. 13. 7 yd

7 yd7 yd

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