Name ________________________________________ Date __________________ Class__________________

Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

10-30 Holt Geometry

Reteach Surface Area of Prisms and Cylinders

The lateral area of a prism is the sum of the areas of all the lateral faces. A lateral face is not a base. The surface area is the total area of all faces.

The lateral area of a right cylinder is the curved surface that connects the two bases. The surface area is the total area of the curved surface and the bases.

Find the lateral area and surface area of each right prism. 1. 2.

_________________________________________ ________________________________________

Find the lateral area and surface area of each right cylinder. Give your answers in terms of !.

3. 4.

_________________________________________ ________________________________________

Lateral and Surface Area of a Right Prism

Lateral Area The lateral area of a right prism with base perimeter P and height h is

L = Ph.

Surface Area The surface area of a right prism with lateral area L and base area B is

S = L + 2B, or S = Ph + 2B.

Lateral and Surface Area of a Right Cylinder

Lateral Area The lateral area of a right cylinder with radius r and height h is

L = 2!rh.

Surface Area The surface area of a right cylinder with lateral area L and base area B is

S = L + 2B, or S = 2!rh + 2!r 2.

lateral face

lateral surface

LESSON

10-4

Name ________________________________________ Date __________________ Class__________________

Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

10-31 Holt Geometry

multiplied by 2.

Reteach Surface Area of Prisms and Cylinders continued

You can find the surface area of a composite three-dimensional figure like the one shown at right.

The dimensions are multiplied by 3. Describe the effect on the surface area.

Find the surface area of each composite figure. Be sure to subtract the hidden surfaces of each part of the composite solid. Round to the nearest tenth. 5. 6.

_________________________________________ ________________________________________

Describe the effect of each change on the surface area of the given figure.

7. The length, width, and height are 8. The height and radius are multiplied by 12

.

_________________________________________ ________________________________________

original surface area: new surface area, dimensions multiplied by 3: S = Ph + 2B S = Ph + 2B = 20(3) + 2(16) P = 20, h = 3, B = 16 = 60(9) + 2(144) P = 60, h = 9, B = 144 = 92 mm2 Simplify. = 828 mm2 Simplify. Notice that 92 x 9 = 828. If the dimensions are multiplied by 3, the surface area is multiplied by 32, or 9.

surface area of

small prism +

surface area of

large prism " hidden

surfaces

LESSON

10-4

Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

A29 Holt Geometry

LESSON 10-4

Practice A 1. L = Ph 2. L = 2!rh 3. S = L + 2B 4. S = 6s2

5. S = 2!rh + 2!r2

6. L = 120 cm2; S = 168 cm2

7. L = 160 m2; S = 280 m2

8. L = 16 ft2; S = 24 ft2

9. L = 8! in2; S = 16! in2

10. L = 60! mm2; S = 78! mm2

11. 384 in2 12. 50.3 in2

13. 6.3 in2 14. 428.0 in2

Practice B 1. L = 176 mi2; S = 416 mi2

2. L = 70 mm2; S = 83.8 mm2

3. L = 1600 in2; S = 2400 in2

4. L = 60! cm2; S = 110! cm2

5. L = 676! ft2; S = 1014! ft2

6. L = 8! m2; S = 40! m2

7. 123.7 km2 8. 113.7 in2 9. The surface area is multiplied by 144. 10. The surface area is divided by 16. 11. 2-by-2-by-2 12. 8-by-1-by-1

Practice C 1. 31,840 mm2

2. The fins greatly increase the surface area of the heat sink. The large surface area allows the heat to be radiated into the air more rapidly.

3. 52 in2 4. 2153.1 m2

5. 48 yd2 6. 1156.1 ft2

7. 45.7 mm2 8. 99.5 cm2

9.

Reteach 1. L = 78 ft2; S = 150 ft2 2. L = 86.8 cm2; S = 96.8 cm2 3. L = 60! in2; S = 110! in2 4. L = 120! cm2; S = 152! cm2 5. S = 68 cm2 6. S " 64.6 in2 7. The surface area is multiplied by 4.

8. The surface area is multiplied by 14

.

Challenge 1. a. 6 b. 8 2. pyramid 3. a. 100 in2

b. 25 3 in2

c. (600 + 200 3 ) in2

4. a. 10 2 in.

b. 2000 2 in3

c. 1253

2 in3

d. 50003

2 in3

5. S = 6n2 + 2n2 3

V = 5 23

n3

6. S = 12m2 + 12m2 2 + 2m2 3

V = 7m3 + 14 23

m3

Problem Solving 1. 275.1 mm2 2. 160 lateral surfaces 3. B 4. G 5. C 6. G

Reading Strategies 1. L = 68 in2

S = 188 in2

2. L = 565.5 cm2

S = 1979.2 cm2

Name ________________________________________ Date __________________ Class__________________

Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

10-46 Holt Geometry

Reteach Volume of Prisms and Cylinders

Find the volume of each prism. 1. 2.

_________________________________________ ________________________________________

Find the volume of each cylinder. Give your answers both in terms of ! and rounded to the nearest tenth.

3. 4.

_________________________________________ ________________________________________

Volume of Prisms

Prism The volume of a prism with base area B and height h is V = Bh.

Right Rectangular Prism

The volume of a right rectangular prism with length A , width w, and height h is V = A wh.

Cube The volume of a cube with edge length s is V = s3.

Volume of a Cylinder

The volume of a cylinder with base area B, radius r, and height h is

V = Bh, or V = !r 2h.

LESSON

10-6

Name ________________________________________ Date __________________ Class__________________

Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

10-47 Holt Geometry

Reteach Volume of Prisms and Cylinders continued

The dimensions of the prism are

multiplied by 13

. Describe the effect

on the volume.

Notice that 216 x 127

= 8. If the dimensions are multiplied by 13

, the volume is multiplied

by 31

3§ ·¨ ¸© ¹

, or 127 .

Describe the effect of each change on the volume of the given figure.

5. The dimensions are multiplied by 2. 6. The dimensions are multiplied by 14

.

_________________________________________ ________________________________________

Find the volume of each composite figure. Round to the nearest tenth.

7. 8.

_________________________________________ ________________________________________

original volume: new volume, dimensions multiplied by 13

:

V = A wh V = A wh

= (12)(3)(6) A = 12, w = 3, h = 6 = (4)(1)(2) A = 4, w = 1, h = 2

= 216 cm3 Simplify. = 8 cm3 Simplify.

LESSON

10-6

Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

A31 Holt Geometry

Problem Solving 1. 16 cm 2. 222.4 mm2

3. 18.7 in. 4. 8 mm 5. D 6. F 7. B 8. G

Reading Strategies 1. Possible answer: it is not perpendicular to

the base, is slanted diagonally, and is the height of a lateral face

2. The base of a pyramid could be different polygons. The base of a cone is always a circle.

3. L = 84.8 cm2

S = 113.1 cm2

4. L = 180 ft2

S = 216 ft2

LESSON 10-6

Practice A 1. V = s3 2. V = Bh 3. V = !r2h 4. V = A wh 5. V = 40 cm3 6. V " 13.5 yd3 7. $162 8. V = 28! m3; V " 88.0 m3

9. V = 200! in3; V " 628.3 in3

10. V = 10 ft3 11. V = 270 ft3

12. The volume is multiplied by 27. 13. V " 114.3 mm3

Practice B 1. V = 42 mi3 2. V " 7242.6 mm3 3. V " 0.4 m3 4. V = 32! yd3; V " 100.5 yd3 5. V = 13.5! km3; V " 42.4 km3 6. V = 810! ft3; V " 2544.7 ft3 7. V " 278.3 cm3 8. The volume is divided by 8. 9. The volume is divided by 125. 10. V " 109.9 ft3 11. V " 166.3 cm3

Practice C 1. 2.6; 2.6 2. 0.62 oz/in3

3. 1.04 in3 4. 28.13 in3

5. a cube with edge length 10 cm 6. 2.5 cm 7. V = 79.3 mm3

8. V = 139.4 ft3

Reteach 1. V = 576 cm3 2. V = 60 in3

3. V = 640! mm3 " 2010.6 mm3

4. V = 45! ft3 " 141.4 ft3 5. The volume is multiplied by 8.

6. The volume is multiplied by 164

.

7. V " 200.3 m3 8. V " 110.0 ft3

Challenge 1. 117h in3 2. 64h in3

3. 55%

4. a. 213

tablespoons

b. 22

c. 12

5 cups

d. 13

3 cups

5. Check students’ work. 6. Multiply the amount of each ingredient by

2117

ab . Round to reasonable measures.

Make sure that c is less than or equal to 2h.

Problem Solving 1. about 23.50 cups 2. about 25 gal 3. B 4. J 5. C 6. F

Reading Strategies 1. V = 512 cm3 2. V " 424.1 in3 3. V = 8000 in3 4. V " 785.4 ft3 5. V = 144 m3

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Volume and Surface Area of Triangular Prisms (A)

Instructions: Find the volume and surface area for each triangular prism.

1) 2)

3) 4)

5) 6)

3.6 km

7.7 km

1.8 km 8.5 km

2.5 cm

5.1 cm 8.5 cm

6.8 cm

8.1 yd 2.1 yd

5.1 yd

7.8 yd

2.02 yd

4.3 m

4.1 m

5.4 m

2.4 m

8.4 m

5.3 mi

3.3 mi

3.6 mi

2.3 mi 1.26 mi

6.2 ft 8.5 ft

5.33 ft

9.8 ft

3.8 ft

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Volume and Surface Area of Triangular Prisms Answer (A)

Instructions: Find the volume and surface area for each triangular prism.

Formula: Volume (V) = 0.5 x bhl, Surface Area (A) = bh+(s1+s2+s3)l

V = 0.5x9.8x5.33x3.8 = 99.2 ft3 A = (9.8x5.33)+((9.8+6.2+8.5)x3.8) = 145.3 ft2

V = 0.5x6.8x5.1x2.5 = 43.4 cm3 A = (6.8x5.1)+((6.8+5.1+8.5)x2.5) = 85.7 cm2

V = 0.5x5.3x1.26x3.3 = 11.0 mi3 A = (5.3x1.26)+((5.3+3.6+2.3)x3.3) = 43.6 mi2

V = 0.5x8.4x2.40x4.1 = 41.3 m3 A = (8.4x2.40)+((8.4+5.4+4.3)x4.1) = 94.4 m2

V = 0.5x3.6x7.7x1.8 = 24.9 km3 A = (3.6x7.7)+((3.6+7.7+8.5)x1.8) = 63.4 km2

V = 0.5x8.1x2.02x5.1 = 41.7 yd3 A = (8.1x2.02)+((8.1+2.1+7.8)x5.1) = 108.2 yd2

1) 2)

3) 4)

5) 6)

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7.7 km

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6.8 cm

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5.1 yd

7.8 yd

2.02 yd

4.3 m

4.1 m

5.4 m

2.4 m

8.4 m

5.3 mi

3.3 mi

3.6 mi

2.3 mi 1.26 mi

6.2 ft 8.5 ft

5.33 ft

9.8 ft

3.8 ft

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Volume and Surface Area of Parallelogram Prisms (A)

Instructions: Find the volume and surface area for each parallelogram prism.

1) 2)

3) 4)

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Volume and Surface Area of Parallelogram Prisms (A)

Instructions: Find the volume and surface area for each parallelogram prism.

1) 2)

3) 4)

V = Area of ABCD x AE = (AB x FI) x AE = (20.0 x 6.5) x 7.3 = 949.0 in3

A = (2x Area of ABCD)+(perimeter of ABCD x AE) = (2x (AB x FI)) + (((2x AB)+(2x BC)) x AE) = (2x (20.0 x 6.5)) + (((2x 20.0)+(2x 8.0)) x7.3) = 668.8 in2

V = Area of ABCD x AE = (AB x FI) x AE = (26.6 x 10.1) x 6.1 = 1638.8 yd3

A = (2x Area of ABCD)+(perimeter of ABCD x AE)

= (2x (AB x FI)) + (((2x AB)+(2x BC)) x AE) = (2x (26.6 x 10.1)) + (((2x 26.6)+(2x 11.1)) x6.1) = 997.3 yd2

V = Area of ABCD x AE = (AB x EI) x FB = (27.2 x 9.1) x 10.1 = 2500.0 m3

A = (2x Area of ABCD)+(perimeter of ABCD x FB)

= (2x (AB x EI)) + (((2x AB)+(2x BC)) x FB) = (2x (27.2 x 9.1)) + (((2x 27.2)+(2x 13.3)) x10.1) = 1313.1m2

V = Area of ABCD x AE = (AB x HI) x HD = (30.0 x 12.2) x 6.1 = 2232.6 ft3

A = (2x Area of ABCD)+(perimeter of ABCD x AE)

= (2x (AB x HI)) + (((2x AB)+(2x BC)) x HD) = (2x (30.0 x12.2)) + (((2x 30.0)+(2x 13.1)) x6.1) = 1257.8 ft2

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Volume and Surface Area of Trapezoid Prisms (C)

Instructions: Find the volume and surface area for each trapezoid prism.

1) 2)

3) 4)

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Volume and Surface Area of Trapezoid Prisms (C)

Instructions: Find the volume and surface area for each trapezoid prism.

1) 2)

3) 4)

V = Area of ABCD x AE = (0.5x(AB + CD)x EI) x AE = (0.5x( 8.1 + 26.3)x21.4) x 3.1 = 1141.0 cm3

A = (2x Area of ABCD)+(perimeter of ABCD x AE)

= (2x (0.5x(AB + CD)x EI)) + (((2x AD)+AB+CD) x AE) = (2x (0.5x(8.1 +26.3)x21.4) + (((2x 22.3)+8.1+26.3) x3.1) = 981.1 cm2

V = Area of ABCD x AE = (0.5x(AB + CD)x GI) x AE = (0.5x( 27.9 + 20.1) x5.1)x 5.2 = 636.5 yd3

A = (2x Area of ABCD)+(perimeter of ABCD x AE)

= (2x (0.5x(AB + CD)x GI)) + (((2x AD)+AB+CD) x AE) = (2x (0.5x(27.9 +20.1) x5.1)+ (((2x 10.1)+27.9+20.1) x5.2) = 599.4 yd2

V = Area of ABCD x AE = (0.5x(AD + BC)x GI) x AE = (0.5x( 30.0 +26.0 ) x12.3)x 10.1 = 3478.4 in3

A = (2x Area of ABCD)+(perimeter of ABCD x AE)

= (2x (0.5x(AD + BC)x GI)) + ((AB+BC+CD+DA) x AE) = (2x (0.5x(30.0+26.0) x12.3)+((12.3+26.0+14.2+30.0) x10.1) = 1522.1 in2

V = Area of ABCD x BF = (0.5x(AB+ CD)x HI) x BF = (0.5x( 25.3 +20.8 ) x11.1)x 4.1 = 1049.0 m3

A = (2x Area of ABCD)+(perimeter of ABCD x BF)

= (2x (0.5x(AB +CD)x HI)) + ((AB+BC+CD+DA) x BF) = (2x (0.5x(25.3+20.8) x11.1)+((25.3+11.1+20.8+12.1) x4.1) = 795.8 m2