CH 12 Test Review Turn Up the Volume and Let s Bend Light Beams Volume and Surface Area of a Prism Vocabulary Write the term from the box that best completes each statement bases of a prism lateral faces of a prism right prism height of a prism oblique prism surface area of a prism lateral edges of a prism prism volume of a prism 1 A(n) is a polyhedron formed by parallelograms The corresponding sides of two congruent and parallel polygons are connected 2 The are the two congruent and parallel faces on a prism 3 The are the parallelograms connecting the corresponding sides of the bases on a prism 4 The are formed by the intersection of the lateral faces on a prism 5 The is the perpendicular distance between the two bases of a prism 6 A(n) is a prism with rectangular faces 7 A(n) is a prism with parallelogram faces 8 The is the amount of space inside a prism 9 The is the total outside area of a prism 1
Backyard Barbecue: Introduction to Volume and Surface Area Calculate the volume of each figure 10 Turn Up the Volume and Let s Bend Light Beams: Volume and Surface Area of a Prism 11 You want to build a storage shed in your back yard for your lawn equipment Two designs for the shed are shown below a What is the volume of Shed A? b What is the volume of Shed B? c Suppose that you want to build a shed that gives you the most space inside Which shed should you choose? 2
Walk in the Footsteps of Archimedes: Volume and Surface Area of a Sphere 12 A can holds 3 tennis balls as shown in the figure The radius of each tennis ball is 3 centimeters a What is the volume of a single tennis ball? b What is the total volume all 3 tennis balls take up? c Can you determine the height of the can? Explain your reasoning d What is the volume of the can? Use 314 forπ e What is the volume of the can not taken up by the tennis balls? Backyard Barbeque: Introduction to Volume and Surface Area Calculate the volume of each rectangular prism V = (8) (2) (5) V = 80 in 3 13 3
14 Backyard Barbeque: Introduction to Volume and Surface Area Calculate the volume of each solid formed by rectangular prisms V = top prism + bottom prism V = (1)(1)(1) + (4)(1)(1) V = 1 + 4 V = 5 ft 3 15 4
16 Backyard Barbeque: Introduction to Volume and Surface Area Calculate the surface area of each rectangular prism SA = front + back + side + side + top + bottom SA = 24 + 24 + 16 + 16 + 6 + 6 SA = 92 m 2 17 5
18 Turn Up the Volume and Let s Bend Light Beams Volume and Surface Area of a Prism Calculate the volume of each right prism V = Bh V = 7 3 V = 343m 3 19 20 6
Turn Up the Volume and Let s Bend Light Beams Volume and Surface Area of a Prism Calculate the surface area of each right prism SA = 2lw + 2wh + 2lh SA = 2(24)(3) + 2(3)(6) + 2(24)(6) SA = 48(3) + 6(6) + 48(6) SA = 144 + 36 + 288 SA = 792 m 2 21 22 7
Modern-Day Pyramids and Soundproofing: Volume and Surface Area of a Pyramid Calculate the volume of each pyramid V = 1 3 Bh V = 1 3 (3)(3)(5) V = 15 m 3 23 24 8
25 Modern-Day Pyramids and Soundproofing: Volume and Surface Area of a Pyramid Calculate the lateral area of each pyramid A = (4) 1 2 (4)(3) A = 24 in 2 26 27 9
Modern-Day Pyramids and Soundproofing: Volume and Surface Area of a Pyramid Calculate the surface area of each pyramid Round to the nearest tenth SA = B + 1 2 Pl SA = (12)(12) + 1 2 (48)(7) SA = 144 + 168 SA = 312 in 2 28 29 10
Modern-Day Pyramids and Soundproofing: Volume and Surface Area of a Pyramid Calculate the total surface area of each composite solid TotalSA = 2(5) 2 + 2(2 8) + 4(5) + 3(4) + 8(4) + 2(4 5) + 2(4 2) = 202 ft 2 30 31 11
Calculate the volume of each cylinder Use 314 forπ Round decimals to the nearest tenth, if necessary V = πr 2 h V = π(55) 2 (7) V = 21175π V 6649 m 3 32 33 34 12
Calculate the surface area of each cylinder Use 314 for Round decimals to the nearest tenth, if necessary SA = 2πrh + 2πr 2 SA = 2π(7)(7) + 2π(7) 2 SA = 196π SA 6154 in 2 35 36 13
37 Calculate the volume of each cone Use 314 for π Round decimals to the nearest tenth, if necessary V = 1 3 πr2 h V = 1 3 π( 5) 2 ( 6) V = 50π V 157 mm 3 38 14
39 40 Use the given dimensions of each cone to calculate the lateral area Use 314 for π Round decimals to the nearest tenth, if necessary The radius of the base is 2 inches The slant height is 101 inches LA = πrl LA 314(2)(101) LA = 634 in 2 41 The radius of the base is 23 meters The slant height is 81 meters 42 The diameter of the base is 6 yards The slant height is 2 yards 15
43 The diameter of the base is 42 inches The slant height is 44 inches Calculate the surface area of each cone Use 314 for π Round decimals to the nearest tenth, if necessary SA = πr 2 + πrl SA = π(5) 2 + π(5)(9) SA = 25π + 45π SA = 70π SA = 2198 in 2 44 45 16
Calculate the volume of each sphere Use 314 for π Round decimals to the nearest tenth, if necessary r = 7 m V = 4 3 πr3 V = 4 3 π( 7) 3 V = 1372 3 π V = 14360 m 3 46 d = 20 in 47 r = 25 cm 48 The radius of the great circle of a sphere is 8 meters 17
49 The diameter of the great circle of a sphere is 20 centimeters Calculate the surface area of each sphere Use 314 forπ Round decimals to the nearest tenth, if necessary r = 4 m SA = 4πr 2 SA = 4π(4) 2 SA = 64π SA 2010 m 2 50 d = 11 m 18
51 r = 25 in 52 The radius of the great circle of a sphere is 5 feet 53 The diameter of the great circle of a sphere is 18 yards 19
Calculate the volume of each sphere given its surface area Use 314 forπ Round decimals to the nearest ten-thousandth, if necessary The surface area of a sphere is 8 square meters SA = 4πr 2 8 = 4πr 2 06369 r 2 07981 r V = 4 3 πr3 V = 4 3 π(07891)3 V 21283 m 3 54 The surface area of a sphere is 10 square inches 55 The surface area of a sphere is 12 square meters 20
ID: A CH 12 Test Review Answer Section 1 ANS: prism PTS: 1 REF: Ch123 TOP: Skills Practice 2 ANS: bases of a prism PTS: 1 REF: Ch123 TOP: Skills Practice 3 ANS: lateral faces of a prism PTS: 1 REF: Ch123 TOP: Skills Practice 4 ANS: lateral faces of a prism PTS: 1 REF: Ch123 TOP: Skills Practice 5 ANS: height of a prism PTS: 1 REF: Ch123 TOP: Skills Practice 6 ANS: right prism PTS: 1 REF: Ch123 TOP: Skills Practice 7 ANS: oblique prism PTS: 1 REF: Ch123 TOP: Skills Practice 8 ANS: volume of a prism PTS: 1 REF: Ch123 TOP: Skills Practice 9 ANS: surface area PTS: 1 REF: Ch123 TOP: Skills Practice 10 ANS: V = 16(10)(22) + 1 2 (16)(6)(22) = 3520 + 1056 = 4576 The volume is 4576 cubic feet PTS: 1 REF: Ch122 TOP: Assignment 1
ID: A 11 ANS: a V = Bh = 8(6)(12) = 576 The volume of Shed A is 576 cubic feet b V = B 1 h 1 + B 2 h 2 = 8(6)(8) + 1 2 (8)(4)(6) = 384 + 96 = 480 The volume of Shed B is 480 cubic feet c You should choose Shed A The volume, or space inside, of Shed A is greater than the volume of Shed B PTS: 1 REF: Ch123 TOP: Assignment 12 ANS: a V = 4 3 πr3 V = 4 3 π Ê Ë Á 33 ˆ 4 3 ( 314) ( 27 ) = 11304 cm3 b Totalvolume = 3(11304) = 33912 cm 3 c Because the 3 tennis balls fit in the can as shown, the can has a height equal to the sum of the diameters of the tennis balls, or 18 centimeters d V = πr 2 h (314)(3 2 )(18) = 50868 cm 3 e The volume of the can that is not taken up by the tennis balls is the difference in volumes, or 50868 33912 = 16956 cubic centimeters PTS: 1 REF: Ch127 TOP: Assignment 13 ANS: V = (2) (35) (8) V = 56 m 3 PTS: 1 REF: Ch122 TOP: Skills Practice 14 ANS: V = (4) (4) (4) V = 64 in 3 PTS: 1 REF: Ch122 TOP: Skills Practice 2
ID: A 15 ANS: V = left prism + middleprism + rightprism V = (2)(6)(1) + (2)(6)(1) + (2)(6)(1) V = 12 + 12 + 12 V = 36 cm 3 PTS: 1 REF: Ch122 TOP: Skills Practice 16 ANS: V = top prism + bottom prism = (12)(1)(2) + (2)(1)(9) = 24 + 18 = 42 ft 3 PTS: 1 REF: Ch122 TOP: Skills Practice 17 ANS: SA = front + back + side + side + top + bottom SA = 66 + 66 + 24 + 24 + 44 + 44 SA = 268 cm 2 PTS: 1 REF: Ch122 TOP: Skills Practice 18 ANS: SA = front + back + side + side + top + bottom SA = 90 + 90 + 27 + 27 + 30 + 30 SA = 294 mm 2 PTS: 1 REF: Ch122 TOP: Skills Practice 19 ANS: V = Bh V = 1 2 (4)(2)(10) V = 40 ft 3 PTS: 1 REF: Ch123 TOP: Skills Practice 20 ANS: V = Bh V = 1 (3 + 9)(2)(62) 2 V = 744 yd 3 PTS: 1 REF: Ch123 TOP: Skills Practice 3
ID: A 21 ANS: SA = 2B + Ph SA = 2 1 (3)(4) + 2(3 + 4 + 5) 2 SA = 12 + 24 SA = 36 in 2 PTS: 1 REF: Ch123 TOP: Skills Practice 22 ANS: SA = 2B + Ph Ê SA = 2 1 ˆ + 8) + 16(5 + 8 + 5 + 14) Ë Á 2 (4)(14 SA = 88 + 512 SA = 600 ft 2 PTS: 1 REF: Ch123 TOP: Skills Practice 23 ANS: V = 1 3 Bh V = 1 Ê 1ˆ 3 Ë Á 2 (4)(6)(10) V = 40 in 3 PTS: 1 REF: Ch124 TOP: Skills Practice 24 ANS: V = 1 3 Bh V = 1 3 ( 8) Ê 1ˆ Ë Á 2 (2)(3)(4) V = 32 cm 3 PTS: 1 REF: Ch124 TOP: Skills Practice 25 ANS: V = 1 3 Bh V = 1 Ê 1ˆ 3 Ë Á 2 (8)(6) ( 5) V = 40 ft 3 PTS: 1 REF: Ch124 TOP: Skills Practice 4
ID: A 26 ANS: A = 4 1 2 (6)(7) A = 84 in 2 PTS: 1 REF: Ch124 TOP: Skills Practice 27 ANS: A = 6 1 2 (6)(8) A = 144 yd 2 PTS: 1 REF: Ch124 TOP: Skills Practice 28 ANS: SA = B + 1 2 Pl SA = 1 2 SA = 7 + 24 SA = 31 cm 2 (4) ( 35 ) + 1 2 (12)( 4) PTS: 1 REF: Ch124 TOP: Skills Practice 29 ANS: SA = B + 1 2 Pl SA = (3)( 3) + 1 2 (12)( 9) SA = 9 + 54 SA = 63 cm 2 PTS: 1 REF: Ch124 TOP: Skills Practice 30 ANS: TotalSA = 5(6) 2 + 4 1 2 (6)(5) = 240 ft 2 PTS: 1 REF: Ch124 TOP: Skills Practice 5
ID: A 31 ANS: Ê SA = 4 1 ˆ Ë Á 2 (8)(6) + 4 Ê 1 ˆ Ë Á 2 (12)(8) SA = 96 + 192 SA = 288 in 2 PTS: 1 REF: Ch124 TOP: Skills Practice 32 ANS: V = πr 2 h Ê V = π 20 ˆ Ë Á 2 V = 500π V 1570 m 3 2 ( 5) PTS: 1 REF: Ch125 TOP: Skills Practice 33 ANS: V = πr 2 h V = π(4) 2 (6) V = 96π V 3014 mm 3 PTS: 1 REF: Ch125 TOP: Skills Practice 34 ANS: V = πr 2 h V = π(45) 2 (12) V = 243π V 7630 m 3 PTS: 1 REF: Ch125 TOP: Skills Practice 35 ANS: SA = 2πrh + 2πr 2 Ê SA = 2π 6 ˆ Ë Á 2 ( 2) + 2π Ê 6 ˆ Ë Á 2 SA = 30π SA 942 ft 2 2 PTS: 1 REF: Ch125 TOP: Skills Practice 6
ID: A 36 ANS: SA = 2πrh + 2πr 2 SA = 2π(4)(74) + 2π(4) 2 SA = 912π SA 2864 cm 2 PTS: 1 REF: Ch125 TOP: Skills Practice 37 ANS: SA = 2πrh + 2πr 2 Ê SA = 2π 5 ˆ Ë Á 2 ( 75) + 2π Ê 5 ˆ Ë Á 2 SA = 50π SA 157 ft 2 2 PTS: 1 REF: Ch125 TOP: Skills Practice 38 ANS: V = 1 3 πr2 h V = 1 3 π(7)2 (10) V = 490 3 π V 5129 ft 3 PTS: 1 REF: Ch126 TOP: Skills Practice 39 ANS: V = 1 3 πr2 h V = 1 3 π( 4) 2 ( 6) V = 32π V 1005 m 3 PTS: 1 REF: Ch126 TOP: Skills Practice 7
ID: A 40 ANS: V = 1 3 πr2 h V = 1 3 π( 3) 2 ( 8) V = 24π V 754 in 3 PTS: 1 REF: Ch126 TOP: Skills Practice 41 ANS: LA = πrl LA 314(23)(81) LA = 585 m 2 PTS: 1 REF: Ch126 TOP: Skills Practice 42 ANS: LA = πrl LA 314(3)(2) LA = 188 yd 2 PTS: 1 REF: Ch126 TOP: Skills Practice 43 ANS: LA = πrl LA 314(21)(44) LA = 290 in 2 PTS: 1 REF: Ch126 TOP: Skills Practice 44 ANS: SA = πr 2 + πrl SA = π(3) 2 + π(3)(4) SA = 9 + 12π SA = 21π SA 659 in 2 PTS: 1 REF: Ch126 TOP: Skills Practice 8
ID: A 45 ANS: SA = πr 2 + πrl SA = π(1) 2 + π(1)(412) SA = π + 412π SA = 512π SA 161in 2 PTS: 1 REF: Ch126 TOP: Skills Practice 46 ANS: V = 4 3 πr 3 V = 4 3 π Ê 20 ˆ Ë Á 2 V = 4000 3 π 3 V 41867 in 3 PTS: 1 REF: Ch127 TOP: Skills Practice 47 ANS: V = 4 3 πr 3 V = 4 3 π(25)3 V = 125 6 π V 654 cm 3 PTS: 1 REF: Ch127 TOP: Skills Practice 48 ANS: V = 4 3 πr3 V = 4 3 π( 8) 3 V = 2048 3 π V 21436 m 3 PTS: 1 REF: Ch127 TOP: Skills Practice 9
ID: A 49 ANS: V = 4 3 πr3 V = 4 3 π( 10) 3 V = 4000 3 π V = 41867 cm 3 PTS: 1 REF: Ch127 TOP: Skills Practice 50 ANS: SA = 4πr 2 = 4π d 2 Ê ˆ Ê = 4π d 2 ˆ Ë Á 2 4 Ë Á = πd 2 SA = π(11) 2 SA = 121π SA 3799 m 2 PTS: 1 REF: Ch127 TOP: Skills Practice 51 ANS: SA = 4πr 2 SA = 4π(25) 2 SA = 25π SA 785 in 2 PTS: 1 REF: Ch127 TOP: Skills Practice 52 ANS: SA = 4πr 2 SA = 4π(5) 2 SA = 100π SA 314 ft 2 PTS: 1 REF: Ch127 TOP: Skills Practice 10
ID: A 53 ANS: SA = 4πr 2 SA = 4π(9) 2 SA = 324π SA 10174 yd 2 PTS: 1 REF: Ch127 TOP: Skills Practice 54 ANS: SA = 4πr 2 10 = 4πr 2 07958 r 2 08921 r V = 4 3 πr3 V = 4 3 π(08921)3 V 29739 in 3 PTS: 1 REF: Ch127 TOP: Skills Practice 55 ANS: SA = 4πr 2 12 = 4πr 2 09549 r 2 09772 r V = 4 3 πr3 V = 4 3 π(09772)3 V 39088 m 3 PTS: 1 REF: Ch127 TOP: Skills Practice 11