MATH 214 Chapter 13
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MATH 214 Chapter 13

Module Code: MAT 214, Spring 2011

University or Institution: Aberystwyth University

Word Count: 741

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Chapter 13-2A 15. Find the cost of carpeting the following rectangular rooms: a) 6.5 m * 4.5 m; cost = $13.85>m2 b) 15 ft * 11 ft; cost = $30>yd2 a) A = 6.5 4.5 = 29.25m 2 Cost = 29.25 13.85 = 405.11 b) A = 15 11 = 165 ft 2 Cost = 165 30 = 4950 20. Find the area of each of the following shaded parts. Assume all arcs are circular with centers marked. Leave all answers in terms of 1. The area of the...

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13-2A Chapter 15. Find the cost of carpeting the following rectangular rooms: a) 6.5 m * 4.5 m; cost = $13.85>m2 b) 15 ft * 11 ft; cost = $30>yd2 a) A = 6.5 4.5 = 29.25m 2 Cost = 29.25 13.85 = 405.11 b) A = 15 11 = 165 ft 2 Cost = 165 30 = 4950 20. Find the area of each of the following shaded parts. Assume all arcs are circular with centers marked. Leave all answers in terms of 1. The area of the entire circle is 4 and the area of each small circle is => The area of the shaded part is 4 - 2 = 2 2. The area of the triangle (2*2)/2 = 1 cm and the are of semicircle is 2 => The area of the shaded part is (1 + ) cm 2 3. The area of the entire circle is 4 and we can observe that the entire circle is shaded by half ( if we switch the shaded part with the part that is not shaded) => The are of shaded part is 2 4. The area of the shaded part is 45.6cm Assessment 13-3A 13.A builder needs to calculate the dimensions of a regular hexagonal window. Assuming the height CD of the window is 1.3 m, find the width AB (O is the midpoint of ) AB in the following figure: x2 + 0.65 2 = > 4 = >4 x 2 = x 2 + 4 0.65 2 x2 = = >3 x 2 = 1.69 = > x 2 = 0.563 = > x = 0.75 We have AC and all of the sides = 0.75 and AI=GB=0.375 => AB=0.75+0.375*2 => AB=1.5 16. A company wants to lay a string of buoys across a lake. To find the length of the lake, they made the following measurements. What is the length of the lake? 180ft 150ft Assume x is the length of the lake We use Pythagoras Theorem for this one too: x = 180 2 150 2 = 32400 22500 = 9900 = 99.5 ft So the length of the lake is 99.5 ft. Assessment 13-4A 2. Find the surface area of each of the following a. The area of the cube is 6a => 64 = 96cm The surface area of the right circular cylinder is : A = 2rh+2r A = 2612+236 A = 216 cm A = 678.6 cm The surface area of right rectangular prism is : A = 2(85+86+56) A = 118 cm The surface area of sphere is : A = 4r A = 64 cm A = 200.96 cm The surface of area right circular cone is : A = r+rl l = 64 + 36 = 10cm => A = 36 + 60 = 96 cm => A = 301.5 cm Assessment 13-5A 13. The Great Pyramid of Cheops is a right square pyramid with height of 148 m and a square base with a perimeter of 940 m. The Transamerica Building in San Francisco has the basic shape of a right square pyramid that has a square base with a perimeter of 140 m and a height of 260 m. Which one has the greater volume and by how many times as great? Since the Great Pyramid of Cheops has a square base with a perimeter of 940 => the length of one side is 940/4 = 235 m 12 1 3 The volume of this pyramid will be V = b h = 55225 148 = 2724433m 3 3 Since the Transamerica Building has a square base with a perimeter of 140 => the length of one side is 140/4 = 35 m 12 1 3 The volume of this pyramid will be V = b h = 1225 260 = 106167 m 3 3 From this measurements => the Great Pyramid of Cheops has a volume of 25.66 times greater than the Transamerica Building in San Francisco. 16. One freezer measures 1.5ft x 1.5ft x 5ft and sells for $350. Another freezer measures 2ft x 2ft x 4ft and sells for $400. Which freezer is the better buy in terms of dollars per cubic foot? 1.5 1.5 5 = 11.25 ft 3 which means that you spend about $31.11 per cubic foot on the first fridge. 350 => = 31.11 11.25 2 2 4 = 16 ft 3 which means that you spend about $25 per cubic foot on the second fridge. 400 => = 25 16 So because you are spending less per cubic foot on the second fridge, this means that the second fridge is the better choice (in terms of price per cubic foot). Note: other factors should be considered when purchasing. 17. A tennis ball can in the shape of a right circular cylinder holds three tennis balls snugly. If the radius of a tennis ball is 3.5 cm, what percentage of the tennis ball can is occupied by air? percentoccupiedbyair=(totalvolumevolumeofballs)/totalvolume =1volumeofballs/totalvolume =13*(4/3) r3/( r2*6r) =14 r3/(6 r3) =14/6 =1/3=33.3%

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