show work for all free response questions 1. Challenge: What is the area of the base of a figure if the volume is 210 ft 3 and the height is 14 ft? QUESTION 2 1. 1. How do you find the volume of a prism or cylinder? QUESTION 3 How do you find the surface area of a cylinder? QUESTION 4 1. 1. How do you find the surface area of a prism? QUESTION 5 Describe what a cylinder is. What are the shapes that make up the different sides? QUESTION 6 1. 1. Find the volume of a cylinder with diameter 22 in and height 15 in. QUESTION 7 Find the surface area of a cylinder with diameter 22 in and height 15 in. QUESTION 8 1. 1. Find the volume of a prism with a square base that is 5 cm by 5 cm and is 10 cm tall. QUESTION 9 Find the surface area of a prism with a square base that is 5 cm by 5 cm and is 10 cm tall. 1. 1. Q U E S T I O N 1 0 - P R I S M S A N D C Y L I N D I R S H O RT Describe what a prism is. How do you know what the base is? How do you know what the height is? When assembled, the following net is a rectangular prism. Find correct answer True Fals e QUESTION 2 1. Find the surface area of the figure below. Find correct answer 25 6 12 8 40 8 31 5 QUESTION 3 1. Find the height of the figure below if the triangle is an equilateral triangle and the surface area is 51.678 mm2. 2.34 2.5 5 3.37 5 1. QUESTION 4 What shapes assemble a cylinder? 1 circle and 2 rectangles 1 circle and 1 rectangle 2 circles and 2 rectangles 2 circles and 1 rectangle QUESTION 5 1. Find the surface area of a cylinder with radius 7 feet and height 16 feet. 1016.1 ft2 322 ft2 505.8 ft2 1011.6 ft2 1. QUESTION 6 The surface area of a cylinder is 289 cm2 and the height is 21 cm. Find the diameter. 2 cm 3 cm 6 cm 4 cm QUESTION 7 1. Find the volume of a rectangular prism that measures 2.7 meters long, 0.9 meters wide, and 0.6 meters high. 145.8 m3 1.458 m3 14.58 m3 0.729 m3 QUESTION 8 1. Find the width of a rectangular prism if the volume is 340, the length is 17, and the height is 5. 8. 5 2 3. 4 4 QUESTION 9 1. Find the volume of the figure below. 165.9 6 166.9 5 169.6 5 196.5 6 QUESTION 10 1. Find the height of a cylinder with a volume of 274.89 and radius of 5. 27.4 ft 25 ft 7 ft 3.5 ft Q U E S T I O N 1 1 - S U R FA C E A R E A A N D V O LU M E O F P R I S M S 1. A cylindrical oil tank with a radius of 5 meters holds 1,000 cubic meters of oil. What is the approximate height of the tank? Use 3.14 for pi, and round your answer to the nearest meter. 1 meters 13 meters 16 meters 32 meters 1. QUESTION 1 Challenge: Find the radius of the base of a cone with volume equal to 144 in 3 and height equal to 12 in. QUESTION 2 1. Find the volume of a cone with radius 30 in and slant height 50 in. QUESTION 3 1. 1. 1. 1. What is the volume of a pyramid that has a base with an area of 81 square feet and a height of 4 feet? QUESTION 4 The base of a pyramid is a square with dimensions 12 in by 12 in. The height of the pyramid is 10 in. What is the slant height of the pyramid? QUESTION 5 If the base of a pyramid is a polygon, what is the shape of all of the sides of the pyramid? How many sides are there (not including the base)? QUESTION 6 How are pyramids and cones different than prisms and cylinders? QUESTION 7 1. 1. 1. Find the surface area of a cone with radius 30 in and slant height 50 in. QUESTION 8 Find the surface area of a pyramid with a square base with dimensions 100 mm by 100 mm and height of 75 mm. Q U E S T I O N 9 P Y R A M I D A N D C O N E S S H O RT 1 0 . 0 2 The base of a cone has a radius of 6 cm. The slant height of the cone is 15 cm. What is the height of the cone? ' 1. QUESTION 1 Which of the following nets, when assembled, results in a pyramid? none of the above all of the above QUESTION 2 1. Find the surface area of the figure below. 200 in2 88 in2 42.5 in2 85 in2 QUESTION 3 1. Find the surface area of the square pyramid below. 1275 mm2 535.5 mm2 2261 mm2 782 mm2 1. QUESTION 4 When assembled, which of the following is a cone? all of the above none of the above QUESTION 5 1. Find the surface area of the figure below. 12.6 5 20.2 9 16.5 6 14.1 1 QUESTION 6 1. Find the surface area of a cone with diameter 18 inches and slant height 22 inches. 452.47 in2 703.04 in2 650.31 in2 876.5 in2 QUESTION 7 1. Find the volume of the figure below. 64 8 68 4 48 6 86 4 1. QUESTION 8 Find the volume of the square pyramid with length 14.7 inches and height 18 inches. 3889.62 in3 1296.54 in3 972.41 in3 1944.81 in3 QUESTION 9 1. Find the volume of the figure below. 0.94 cm3 2.81 cm3 1.41 cm3 0.84 cm3 QUESTION 10 1. Find the volume of the figure below. 1654 m3 8063.49 m3 16126.97 m3 5375.66 m3 Q U E S T I O N 1 1 - 1 0 . 0 2 S U R FA C E A R E A V O LU M E A N D P Y R A M I D AND CONES 1. Find the volume of this oblique pyramid. 160 cubic units 320 cubic units 480 cubic units 640 cubic units Question 1 1. Find the surface area of a sphere with a volume of 36 in3. 3 points 1. QUESTION 2 Challenge: The distance around the middle of a sphere (the circumference) equals 37.699 in. What is the surface area of the sphere? 3 points QUESTION 3 1. Find the volume of a sphere with surface area equal to 100 ft 2. 3 points QUESTION 4 1. Find the diameter of a sphere with a volume equal to 14,137.167 cm3. 3 points QUESTION 5 1. Challenge: The distance around the middle of a sphere (the circumference) equals 25.1327 in. What is the volume of the sphere? 3 points QUESTION 6 1. In your own words, define a sphere. 3 points QUESTION 7 1. Find the surface area of a sphere with radius 7 in. 3 points QUESTION 8 1. Find the volume of a sphere with diameter 21 cm. 3 points QUESTION 9 1. 1. How do you find the surface area of a sphere? What should the label be? Q U E S T I O N 1 0 - S P E H E R E S H O RT A N S W E R How do you find the volume of a sphere? What should the label be? Question 1 The following, when assembled, is a sphere. True Fals e 1. QUESTION 2 Find the surface area of a sphere with radius 8.4 inches. 221.67 in2 105.56 in2 886.68 in2 282.24 in2 1. QUESTION 3 Find the surface area of a sphere with diameter 17 cm. 907.92 cm2 226.98 cm2 289 cm2 106.81 cm2 QUESTION 4 1. Find the length of the radius of a sphere with a surface area of 314.16 ft 2. 5 ft 15 ft 10 ft 2.5 ft 1. QUESTION 5 Find the length of the diameter of a sphere with a surface area of 490.87 km2. 12.5 km 25 km 6.25 km 3.125 km QUESTION 6 Find the volume of the figure below. 1436.76 ft3 457.33 ft3 808.17 ft3 205.25 ft3 1. QUESTION 7 Find the volume of a sphere with radius 1.5 km. 5.3 km3 28.29 km3 7.96 km3 14.14 km3 QUESTION 8 1. Find the volume of a sphere with diameter 2.3 cm. 6.37 cm3 35.26 cm3 14.14 cm3 28.28 cm3 1. QUESTION 9 Find the length of the diameter of a sphere with a volume of 143.8 miles 3. 5.86 miles 3.25 miles 6.5 miles 11.72 miles QUESTION 10 1. Find the length of the radius of a sphere with a volume of 904.78. 6 14. 7 12 29. 4 Q U E S T I O N 1 1 - S U R FA C E A R E A A N D V O LU M E F O R S P E H R E What is the heating capacity, in BTUs, of a spherical tank of natural gas with a radius of 3 feet? Assume that 1 cubic foot of natural gas contains 1,030 BTUs. Use 3.14 for pi, and round your answer to the nearest BTU. 283 BTU 97, 026 BTU 116,431 BTU 711, 022 BTU 1. Find the surface area of the figure below. 63.84 ft2 127.68 ft2 84.67 ft2 254.02 ft2 2 points QUESTION 2 1. Find the surface area of the right triangular prism below. 436.278 in2 466.97 in2 332.94 in2 253.46 in2 2 points QUESTION 3 1. Find the value of p in the right triangular prism if the surface area is 432 in 2. 16 in 15 in 24 in 9 in 2 points 1. QUESTION 4 Find the height of a rectangular prism if the surface area is 148 cm2, the width is 4 cm and the length is 5 cm. 3 points QUESTION 5 1. Find the surface area of the figure below. 9.74 square units 6.20 square units 19.48 square units 12.40 square units 2 points QUESTION 6 1. Find the surface area of a cylinder with diameter 24 mm and height 16 mm. 1055.58 mm2 2111.15 mm2 672.00 mm2 1344.00 mm2 2 points 1. QUESTION 7 Find the height of a cylinder with radius 2.5 cm and surface area 88.59 cm 2. 10.0 cm 5.0 cm 6.28 cm 3.14 cm 2 points QUESTION 8 1. Find the height of the figure below if the surface area is 119.38 mm2. 3 points QUESTION 9 1. Find the volume of the figure below. 106.79 mi3 67.98 mi3 213.57 mi3 135.96 mi3 2 points QUESTION 10 1. Find the volume of a rectangular prism that measures 4.77 meters long, 2.49 meters wide, and 3.47 meters high. 41.21 m3 20.61 m3 82.42 m3 27.47 m3 2 points QUESTION 11 1. Find the value of x in the figure below if the volume is 676.2 ft 3. x= 55.2 x= 27.6 x= 24.5 x = 49 2 points QUESTION 12 1. Find the value of x in the figure below if the volume is 44.96 m3. x= 24.3 x = 7.4 x = 3.7 x= 12.15 2 points 1. QUESTION 13 Find the width of a rectangular prism if the volume is 77,680 cm3, the length is 43 cm, and the height is 94.4 cm. 3 points QUESTION 14 1. The following net, when assembled, is a cylinder. True Fals e 2 points QUESTION 15 1. Find the volume of the figure below. 112.00 ft3 175.93 ft3 351.86 ft3 224.00 ft3 2 points 1. QUESTION 16 Find the volume of a cylinder with height 14 cm and diameter 10 cm. 549.78 cm3 2199.12 cm3 1099.56 cm3 350.00 cm3 2 points QUESTION 17 1. Find the height of the figure below if the volume is 135.33 cm3. 7.8 cm 5.52 cm 11.04 cm 15.6 cm 2 points QUESTION 18 1. Find the radius of a cylinder with a volume of 118.79 feet 3 and height of 5 feet. 3 points QUESTION 19 1. The following net, when assembled, is a pyramid. True Fals e 2 points QUESTION 20 1. Find the area of the square pyramid below. 126 mm2 175 mm2 490 mm2 245 mm2 2 points 1. QUESTION 21 Find the surface area of a square pyramid that has a side length of 15 ft and slant height of 19 ft. 160.8 ft 367.5 ft2 1365 ft2 795 ft2 2 points 1. QUESTION 22 Find the surface area of the pyramid with square base that measures 8 ft by 8 ft and slant height of 12 ft. 3 points QUESTION 23 1. Find the surface area of the figure below. 340.00 m2 2616.95 m2 3925.43 m2 1308.48 m2 2 points QUESTION 24 1. Find the surface area of the figure below. 790.90 cm2 395.45 cm2 1186.35 cm2 95.0 cm2 2 points QUESTION 25 1. Find the slant height of a cone with surface area 1861.39 ft2 and radius 15 ft. 24.5 ft 12.25 ft 30 ft 47.12 ft 2 points 1. QUESTION 26 Find the slant height of a cone with surface area 282.74 ft 2 and diameter 10 ft. 3 points QUESTION 27 1. Find the volume of the figure below. 1944 in3 3240 in3 1296 in3 1620 in3 2 points QUESTION 28 1. Find the volume of the figure below. 3441.24 in3 5161.86 in3 3872 in3 1547.19 in3 2 points 1. QUESTION 29 Find the height of a square pyramid with volume 96 m 3 and dimensions of base are 9 m by 9 m. 7.11 m 5.24 m 3.56 m 1.19 m 2 points 1. QUESTION 30 Find the height of a square pyramid with volume 243.73 ft3 and dimensions of base are 7.5 ft by 7.5 ft. 13 ft 8.67 ft 4.33 ft 9 ft 2 points 1. QUESTION 31 Find the height of a square pyramid with volume 26.97 ft 3 and dimensions of base are 3 ft by 3 ft. 3 points QUESTION 32 1. The following net, when assembled, is a cone. True Fals e 2 points QUESTION 33 1. Find the volume of the figure below. 117.17 cm3 298.37 cm3 938.29 cm3 2814.87 cm3 2 points QUESTION 34 1. Find the volume of the figure below. 14.21 units3 4.73 units3 44.66 units3 14.89 units3 2 points 1. QUESTION 35 Find the height of a cone with volume 876.80 cm3 and radius 7.5 cm. 14.89 cm 58.85 cm 7.45 cm 87.68 cm 2 points QUESTION 36 1. Find the radius of a cone with volume 199.23 cm3 and height 9 cm. 3 points QUESTION 37 1. Find the surface area of the figure below. 4071.5 m2 1017.88 m2 9160.88 m2 73287.07 m2 2 points 1. QUESTION 38 Find the surface area of a sphere with diameter 8.6 ft. 232.35 ft2 929.41 ft2 799.2 ft2 999.11 ft2 2 points QUESTION 39 1. Find the surface area of a sphere with diameter 10.5 feet. 1818.39 ft2 346.36 ft2 14547.14 ft2 1385.44 ft2 2 points QUESTION 40 1. Find the length of the radius of a sphere with a surface area of 5541.77 cm 2. 21 cm 11.5 cm 42 cm 37 cm 2 points 1. QUESTION 41 Find the length of the diameter of a sphere with a surface area of 50.27 ft 2. 1.77 ft 3.54 ft 2 ft 4 ft 2 points QUESTION 42 1. All points on a sphere are equidistant from the center of the sphere. True Fals e 2 points QUESTION 43 1. Find the volume of the figure below. 767.41 ft3 10,305.99 ft3 5797.12 ft3 3280.5 ft3 2 points QUESTION 44 1. Find the volume of a sphere with radius 2.5 miles. 36.82 miles3 26.2 miles3 65.45 miles3 20.83 miles3 2 points 1. QUESTION 45 Find the length of the diameter of a sphere with a volume of 523.6 km3. 5 km 11.2 km 10 km 22.4 km 2 points Q U E S T I O N 4 6 - U N I T 1 0 V O LU M E A N D S U R FA C E A R E A 1. Find the length of the radius of a sphere with a volume of 1436.76 in 3. 18.5 in 7 in 37 in 14 n Question 1: Describe in your own words what a translation is. 3 points QUESTION 2 1. How are the coordinates of the new point found if it is translated right/left and up/down? 3 points QUESTION 3 1. There are three ways to denote a translation. What are the three ways? 3 points QUESTION 4 1. What is (-1, -2)? 3 points QUESTION 5 1. Start with the point A (3, 1). Translate the point 1 unit to the left and 4 units down. What are the new coordinates of the point A'? Now translate A' 3 unit to the left and 2 units up. What are the new coordinates of the point A''? What translation would need to be made in order for the result to be the original point A (3, 1)? 3 points QUESTION 6 1. Describe in your own words what a reflection is. 3 points QUESTION 7 1. How are the coordinates of the new point found if it is translated right/left and up/down? 3 points QUESTION 8 1. How are the coordinates of a new point found if the point is reflected through the line y = x? How are the coordinates of the new point found if the point is reflected through the origin? 3 points QUESTION 9 1. The point X (-3, 6) is a reflection of the point X' (3, -6). What are they reflected through? 3 points QUESTION 10 1. 1. Start with the point B (-1, -4). Reflect the point through the y-axis. What are the new coordinates of the point B'? Now reflect the point through the x-axis. What are the new coordinates of the point B''? What is the relationship between the original point B and B''? Can you describe this in terms of one reflection QUESTION 1 Define translation. A translation is a type of transformation that can be defined as an image rotated across a line or a point. A translation is a type of transformation that moves a figure to a new location with no change to the size or shape of the figure. A translation is a type of transformation that reduces or enlarges the figure to a similar figure. A translation is a type of transformation that can be defined as a mirror image seen across a line or a point. 2 points QUESTION 2 1. Which of the following is an example of a translation? 2 points 1. QUESTION 3 Quadrilateral WXYZ is located at W(2,1), X(5,2), Y(4,4), Z(2,4). A translation of the quadrilateral is located at W'(5, 5), X'(8, 6), Y'(7, 8), Z'(5, 8). How is the quadrilateral translated? Quadrilateral units up. Quadrilateral units up. Quadrilateral units down. Quadrilateral units down. WXYZ is translated 3 units to the right and 4 WXYZ is translated 4 units to the right and 3 WXYZ is translated 3 units to the left and 3 WXYZ is translated 4 units to the left and 3 2 points QUESTION 4 1. Under the translation T(9, -2) the point (-3, -6) will become (6, -8). True Fals e 2 points QUESTION 5 1. If the following object is translated (x + 2, y - 3), where will the translation be located? 2 points QUESTION 6 1. What type of transformation can be defined as a mirror image seen across a line or a point? reflectio n translati on dilation rotation 2 points QUESTION 7 1. Which of the following is a real-life example of a reflection? looking in a mirror going down a water slide blowing up a balloon climbing a tree 2 points 1. QUESTION 8 Which of the following sets of points are reflections of each other across the x-axis? (2, 3) -3) (2, 3) -3) (2, 3) 3) (2, 3) -2) (-2, (2, (-2, (-3, 2 points QUESTION 9 1. If triangle ABC is reflected across line m, where will the new coordinates be located? A'(-2, 4); C'(2, 8) A'(7, -8); 2, -8) A'(2, -4); C'(7, -8) A'(2, -4); 2, -9) B'(-7, 8); B'(2, -4); C'(B'(-2, -8); B'(7, -9); C'(2 points Q U E S T I O N 1 -T R A N S L AT I O N / F E L F E C T I O N Q U I Z 1. How many lines of symmetry does the following figure have? There is one line of symmetry There are two lines of symmetry There are four lines of symmetry There are no lines of symmetry 1. A rotation is a type of transformation that turns the figure clockwise or counterclockwise but does not change the figure. True Fals e 2 points 1. QUESTION 2 Which of the following is an example of a rotation? 2 points 1. QUESTION 3 Point A is located at (3, 4) and is rotated 90 counterclockwise about the origin. What is the new location of point A? (-3,4) (4, 3) (-4, 3) (4, -3) 2 points QUESTION 4 1. When point E (-6, 2) is rotated 270 counterclockwise about the origin, its coordinate becomes Point E' (2, 6). True Fals e 2 points QUESTION 5 1. If the figure below is rotated 180, what is the new location? A'(-8, 0); B'(0, 6); D'(0, -6) A'(0, 8); B'(-6, 0); D'(6, 0) A'(0, -8); B'(6, 0); D'(-6, 0) A'(8, 0); B'(0, -6); D'(0, 6) C'(8, 0); C'(0, -8); C'(0, 8); C'(-8, 0); 2 points QUESTION 6 1. Define enlargement and reduction. A dilation is a type of dilation where the value of the scale factor is greater than 0. An enlargement is a type of dilation where the value of the scale factor is less than 0. A dilation is a type of dilation where the absolute value of the scale factor is greater than 1. An enlargement is a type of dilation where the absolute value of the scale factor is between 0 and 1. An enlargement is a type of dilation where the value of the scale factor is greater than 0. A reduction is a type of dilation where the value of the scale factor is less than 0. An enlargement is a type of dilation where the absolute value of the scale factor is greater than 1. A reduction is a type of dilation where the absolute value of the scale factor is between 0 and 1. 2 points QUESTION 7 1. Which of the following is an example of a dilation? 2 points QUESTION 8 1. Find the measure of the dilated image of segment CD, 5 units long, with a scale factor of 4. 1 20 2 points QUESTION 9 1. The length of a rectangle is 48 in and is dilated to 12 in. What is the scale factor? -4 4 2 points QUESTION 10 1. Under a dilation, triangle XYZ where X(6, 3), Y(-2, 4), and Z(10, -2) becomes triangle X'Y'Z' where X'(3, 1.5), Y'(-1, 2), and Z'(5, -1). What is the scale factor for this dilation? -2 2 2 points QUESTION 11 1. Consider line segment AB whose endpoints are (1, 4) and (4, 8). If this segment is dilated by a scale factor of 3 centered at the origin, find the length of the new segment, A'B'. 3 5 9 1 5 2 points Q U E S T I O N 1 2 - R O TAT I O N / D I A L AT I O N 1. The image of a reflection is always smaller than the pre-image. True Fals e Question 1 1. How are the coordinates of the new point found if it is rotated 90 counterclockwise? How many degrees is that equivalent to if the rotation is clockwise? 3 points QUESTION 2 1. How are the coordinates of the new point found if it is rotated 180 counterclockwise? How many degrees is that equivalent to if the rotation is clockwise? 3 points 1. QUESTION 3 Describe in your own words what a rotation is. 3 points QUESTION 4 1. A triangle has coordinates A (1, 5), B (-2, 1) and C (0, -4). What are the new coordinates if the triangle is dilated with a scale factor of ? 3 points 1. QUESTION 5 A line segment has endpoints P (3, 6) and Q (12, 18) and is dilated so that its new endpoints are P' (2, 4) and Q' (8, 12). What is the scale factor? If the length of PQ is 15, what is the length of P'Q'? 3 points 1. QUESTION 6 A triangle has coordinates A (1, 5), B (-2, 1) and C (0, -4). What are the new coordinates if the triangle is rotated 90 clockwise around the origin? 3 points QUESTION 7 1. How are the coordinates of the new point found if it is rotated 270 counterclockwise? How many degrees is that equivalent to if the rotation is clockwise? 3 points 1. QUESTION 8 How are the coordinates of the new point found if it is dilated with a scale factor of 3? 3 points Q U E S T I O N 9 - R O TAT I O N A N D D I A L AT I O N S H O RT A N S W E R 1. Describe in your own words what a dilation is