Geometry Review 4 G.C.5 Answers

GEOMETRY Review #4 G.C.5 Answers all WEBSITE 1. C 5. a. 2. C 45 i16p = 2p » 6.28 360 90 Sector BOC : i16p = 4p » 12.56 360 60 8p Sector COD : i16p = » 8.37 360 3 35 14p Sector DOE : i16p = » 4.88 360 9 mÐAOE = 360° - 45° - 90° - 60° - 35° mÐAOE = 130° 130 52p Sector AOE : i16p = » 18.14 360 9 b. 6.28 + 12.56 + 8.37 + 4.88 + 18.14 = 50.23 Area of the circle = r2 = 16  50.24 (The slight difference in these values is due to the rounding in part a) Sector AOB : 3. No, Raoul is not correct. If the central angle of the sector is m, then the area of m ip r 2 . The area 360 m of the new sector is ip (4r )2 , or 360 m 16 i ip r 2 . The area is multiplied by 360 the original sector is 16, not 4. Rubric 1 point for saying Raoul is incorrect; 2 points for explanation 4. Suppose the measure of AB and CD is m. m i2p r 360 m = i6p 360 Arc length of AB = = p 60 m m i2p r 360 m = i10p 360 Arc length of CD = = p 36 m p m 5 = 36 = . Arc length of AB p m 3 60 Arc length of CD Thus, the equation is arc length of CD = 5 iarc length of AB. 3 Rubric 1 point for answer; 2 points for appropriate work Rubric a. 0.5 point for each sector area b. 0.5 point for finding the sum of the sector areas; 1 point for comparison to area of full circle 6. a. radius, r arc length, s 2 3 4 5 2 p 3  4 p 3 5 p 3 b. c. The relationship is a proportional relationship, and the constant of proportionality is p . 3 Rubric a. 0.5 point for each arc length b. 1 point for plotted points; 1 point for line through the origin c. 1 point G.GPE.1 Answers 1. A, C, F 2. C 3. C 4. F 7. E 8. D G.GPE.4 Answers 1. C 2. B 3. a. b. c. d. e. On the circle Inside the circle Inside the circle On the circle Outside the circle 5. The midpoint of GH is æ-2 + 4 -6 + 1æ , = (1, - 2.5). æ 2 æ æ 2 æ The x-coordinate is positive, and the y-coordinate is negative, so the point is in quadrant IV. G.GPE.5 Answers G.GPE.4 Answers Rubric 2 points for finding the midpoint; 1 point for explaining why it lies in quadrant IV Rubric a. 2 points for appropriate calculations; 1 point for explanation b. 1 point c. 1 point for correctly changing the coordinates of one point; 2 points for showing that DEFG is a parallelogram G.GPE.5 Answers 6. Slope of line m: 1. C 2. B 3. A, D 9 -1 8 4 = =3 - 9 -6 3 2 - 8 -6 3 Slope of BD : = = 2 - 10 -8 4 4 3 - • = -1, so AC ^ BD , and AC and 3 4 5. Slope of AC : BD intersect at a right angle. Rubric 1 point for each slope; 1 point for showing AC ^ BD ; 1 point for concluding AC and BD intersect at a right angle Slope of line n: 3-2 1 1 = =0 - 3 -3 3 0 - (-1) 1 1 = =-3 - 0 -3 3 The slopes of the lines are equal; therefore, the lines are parallel. When two parallel lines are cut by a transversal, alternate exterior angles are congruent. Therefore, 1  7. Rubric 1 point for each slope; 1 point for showing that m n ; 1 point for concluding that 1  7 Rubric 1 point for answer; 1 point for appropriate work G.GPE.6 Answers 1. A 2. D 3. A, B, D 4. D The coordinates of point P are æ 4 4 æ æ 6æ -2 + [7], - 5 + [2]æ = æ2, - 3 æ. æ 7 7 æ æ 7æ æ Rubric 1 point for finding the coordinates of P; 1 point for showing work 5. F 6. G 7. A 8. SP is 4 4 = of ST. 4+3 7 Run of ST: 5 − (−2) = 7; rise of ST: −3 − (−5) = 2 G.GPE.7 Answers 1.B, C, D 2. B 3. B G.GMD.1 Answers G.GMD.1 Answers 1.C 2. C 3. A, B, E G.GMD.3* Answers G.GMD.3* Answers 1.B 2. A 3. G 4. H 5. D 6. A 7. A, C, E 8. The volume of the cylinder is about 62.8 in3. V = p r 2h = p (2)2 (5) = 20p » 62.8 Rubric 1 point for answer; 1 point for showing work G.GMD.4 Answers 1. B 2. B 3. A, B, C 6. The polygon can have at most 6 sides. A rectangular prism has 6 faces, and a plane cannot intersect a face more than once, so the greatest number of possible sides is 6. 5. Both rotations generate a cone. However, the cones do not have the same radius and height. The radius of the first cone is 3 and the height is 4. The second cone has radius 4 and height 3. Rubric 1 point for stating that both rotations generate cones; 2 points for stating that the dimensions of the cones are different Rubric 1 point for answer; 2 points for accurate diagram G.MG.1* Answers 1.B 2. A 3. A, B, D 4. Before it is sharpened, the pencil is best modeled by a cylinder. After it is sharpened, the pencil is best modeled by a cylinder with a cone on top, because the sharpened part of the pencil resembles a cone. Rubric 1 point for model before; 1 point for model after; 1 point for explanation 5. a. A rectangular prism is the closest in shape to a box of cereal. b. Yes. Because all the boxes are the same size, packing them in the manner described creates a larger rectangular prism. Rubric a. 1 point b. 1 point for answer; 1 point for explanation 7. The top and bottom bases of the wooden section are rectangles. The lateral faces of the wooden section are four isosceles trapezoids. Rubric 1 point for describing bases; 1 point for describing lateral faces G.MG.1* Answers G.MG.2* Answers 1. B 3. A, B 4. a. b. c. d. e. Less than Greater than Greater than Less than Less than G.MG.3* Answers 1. B 2. C 3. C 4. B, C, E 5. The height of the cylinder is the same as the diameter, so the height is twice the radius. The volume of the cylinder is V = r2h = r2(2r) = 2r3. Teresa forgot to include a factor of 2 in her formula for the volume of the cylinder. 2p r 3 = 300 p r 3 = 150 r 3 » 47.75 r » 3.6 The radius of the cylinder is about 3.6 cm. Rubric 1 point for finding the mistake; 1 point for correct radius; 1 point for work