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Nameclass49. A plane intersects this rectangular prism and formsa cross section. Which shape CANNOT be a crosssection of the prism?47. In the diagram, ABCDE and FGHJK are congruentregular pentagons.ABEdateCDFGKHJa. What is the shape of the cross section made by aplane that is parallel to the base?A. triangleB. circleC. rectangleD. square50. Construct viable arguments. Can you create apolyhedron with 9 vertices and 16 edges? Justifyyour reasoning.b. What is the shape of the cross section made by aplane that contains points A, C, and J?Lesson 33-251. Which statement describes a figure that can beformed using the net shown?c. What shapes are in the net of the prism, andhow many of each kind are there?6p33d. How many vertices, edges, and faces does theprism have?A. The figure is a cylinder whose base has acircumference of 6 and whose height is 6p.B. The figure is a cylinder whose base has acircumference of 6p and whose height is 6.48. A prism has 18 edges and 8 faces. How manyvertices does the prism have?C. The figure is a cylinder whose base has acircumference of 6p and whose height is 6p.D. The figure is a cone whose base has a radius of3 and whose height is 6p. 2015 College Board. All rights reserved.9SpringBoard Geometry, Unit 5 Practice

Nameclass52. A plane intersects the cylinder shown.date54. Model with mathematics. The diagram shows acone and a net of the cone.ZAXCa. What is the shape of the cross section if theplane is parallel to the bases?BWDYa. Which point on the cone corresponds withpoint X on the net?b. What is the shape of the cross section if theplane is perpendicular to the bases?b. Which segment on the net represents thedistance from A to C on the cone?c. On the net, which distance is equal to thecircumference of circle D?c. Can a cross section of the cylinder be asegment? Explain your answer.d. What distance on the cone is the same as thedistance from W to D on the net?55. Reason quantitatively. The right cone shown hasa height of 6 cm and a base with a radius of 8 cm.d. Suppose a plane is perpendicular to the base.Are cross sections that contain the center of thebase different from cross sections that do notcontain the center of base? Explain.6 cm8 cm53. What shapes are used in a net for a cylinder? Howare those shapes related to each other?a. What is the exact value of the circumference ofthe base?b. A plane parallel to the base intersects the coneat a distance of 3 cm from the vertex. What is anexact value for the area of the cross section? 2015 College Board. All rights reserved.10SpringBoard Geometry, Unit 5 Practice

Nameclassdatec.Lesson 33-35 in.56. A plane intersects a sphere. State whether or notthe plane contains the center of the sphere in eachsituation.2 in.a. The cross section is a great circle of the sphere.b. The cross section is not a great circle of thesphere.d.57. The cross section of a sphere and a plane is a point.Describe the relationship between the plane andthe sphere.2 in.59. Which of the following statements is NOT true?58. The diagram below shows rectangle ABCD andlines ℓ, m, n, p, and q, which are possible lines ofrotation of the rectangle. AB is 5 in. and BC is 2 in.The solids of rotation below were formed fromABCD. Identify the line that was used as the axis ofrotation for each solid.nmA. A chord of a sphere can have the same length asthe radius of the sphere.B. The diameter of a sphere must contain thecenter of the sphere.C. The intersection of a plane and a sphere isalways a great circle.pAB5 in.D. A sphere can be generated by rotating a circlearound its diameter.lqDCa.60. Make use of structure. A solid of rotationisformed by rotating nABC around AB.a. What shape is formed?10 in.b. What measurement ofthe solid is AB?2 in.b.A5 in.c. What measurement ofthe solid is BC?4 in.BCd. What distance on the solid is equal to AC? 2015 College Board. All rights reserved.11SpringBoard Geometry, Unit 5 Practice

Nameclassdate63. Reason quantitatively. A triangular prism has abase that is an isosceles triangle with sides 13 cm,13 cm, and 24 cm. The height of the prism is 10 cm.Lesson 34-161. A net for a cylinder is shown below. The diameterof each base and the height of the cylinder are6 cm. Find each measure to the nearest tenth.24 cm10 cm13 cm13 cma. Find the lateral area of the prism.a. Find the circumference of each circle in the net.b. What are the dimensions of the rectangular partof the net?c. In the net, find the area of each circle and thearea of the rectangular part.b. Find the total surface area of the prism.d. What is the surface area of the cylinder?62. An isosceles trapezoid has bases 15 in. and 9 in.,and a height of 4 in. The trapezoid is the base of aprism with a height of 5 in.a. What is the length of each leg of the trapezoidalbase?b. What is the perimeter of the trapezoidal base?64. Which statement about the surface area of a prismis NOT true?c. What is the lateral area of the prism?A. The surface area is (area of base) 1(area of base) 1 (lateral area).d. What is the area of each base of the prism?B. The surface area is (perimeter of prism) ?(height of prism) ? (area of base).e. What is the total surface area of the prism?C. The lateral area is the sum of the areas of thelateral surfaces.D. The lateral area is (perimeter of base) ?(height of prism). 2015 College Board. All rights reserved.12SpringBoard Geometry, Unit 5 Practice

Nameclassdate68. Consider the two cylinders shown.65. Attend to precision. A cylinder is cut through acube. The side of the cube is 10 cm and thediameter of the hole is 4 cm. Write exact values foreach measurement.210 cm4 cm4416Which statement is true?a. the lateral area of the cylinderA. The two cylinders have the same base area.B. The two cylinders have the same lateral area.b. the lateral area of the cubeC. The two cylinders have the same surface area.D. The two cylinders have the same volume.c. the area of the top of the cube, not counting thecircular hole69. Model with mathematics. Find each missingmeasurement.d. the total surface area of the object, including thelateral area of the cylinder inside the cubea. Find the radius of a cylinder if the cylinder has aheight of 3 cm and a volume of 75p cm3.Lesson 34-266. The total surface area of a cube is 294 m2. What isthe volume of the cube?b. Find the height of a prism if the base is a righttriangle with legs 3 in. and 5 in., and the volumeof the prism is 150 in.3.67. A square prism has a base with 8-in. sides and atotal surface area of 288 in.2. What is the volume ofthe prism? 2015 College Board. All rights reserved.13SpringBoard Geometry, Unit 5 Practice

Nameclass70. Attend to precision. A cylindrical water tank isshown. The diameter of the base is 8 ft and thecylinder is 16 ft long. The cylinder is exactly halffilled with water.date72. Persevere in solving problems. A cone has aradius of 12 units and a slant height of 15 units.Write each measurement as an exact value.a. the area of the base of the coneb. the lateral area of the cone8 ftc. the surface area of the cone16 ftd. the height of the conea. How many cubic feet of water are currently inthe tank? Write your answer to the nearesthundredth of a cubic foot.73. Use the given measures of each cone to find anexact value for the missing measure.lhb. Water is filling the tank at a rate of 3 ft3 perminute. In how many minutes will the tank befull? Write your answer to the nearest minute.ra. r 5 5 cm, ℓ 5 8 cm; find the lateral areaLesson 35-171. Each of these sectors represents the lateral area of acone. As the angle between the two radii increases,which of the following does NOT increase?b. ℓ 5 10 in., h 5 6 in.; find the area of the basec. h 5 8 cm, r 5 8 cm; find the total surface areaA. the lateral area of the coned. total surface area 5 84p cm2, ℓ 5 8 cm; find rB. the area of the base of the coneC. the height of the coneD. the slant height of the cone 2015 College Board. All rights reserved.14SpringBoard Geometry, Unit 5 Practice

Nameclass74. The figure shown is formed by a cylinder and acone that have the same height and the samediameter. Write an exact value for each measure.Lesson 35-276. How is the volume of a prism related to the volumeof a pyramid that has the same base and sameheight?10 cm4 cmdate10 cmhhBa. the area of the baseb. the lateral area of the cylinderBA. The volumes are not related to each other.B. The volumes are equal.c. the slant height of the coneC. The volume of the prism is two times thevolume of the pyramid.d. the lateral area of the coneD. The volume of the prism is three times thevolume of the pyramid.e. the total surface area of the figure77. Express regularity in repeated reasoning.Consider a square pyramid.75. Attend to precision. A surveyor’s pendant is asmall weight that hangs from a string and is used toestablish vertical lines. The pendant shown belowis formed from two congruent cones. The radiusand height of each cone is 3 cm.h3 cmls3 cm3 cma. Find the volume of the pyramid if a side of thebase is 8 cm and the height is 12 cm.a. Find the slant height of each cone to the nearesthundredth.b. Find the slant height and the volume of apyramid if the base has an area of 36 cm2 and aheight of 4 cm.c. Find a side of the base if the volume is 245 in.3and the height is 15 in.b. Find the total surface area of the surveyor’spendant to the nearest hundredth.d. Find the volume if the slant height is 8 units andthe height is 6 units. 2015 College Board. All rights reserved.15SpringBoard Geometry, Unit 5 Practice

Nameclassdate80. A student knows the height of a pyramid and thearea of its base. What should the student do to findthe volume of the pyramid?78. A cone has a volume of 300 cm3. Find eachmeasure to the nearest tenth.a. the height of the cone if the radius of the baseis 8 cmA. Add the height and the area.B. Find one third of the sum of the heightand area.b. the radius of the base if the height of the coneis 10 cmC. Multiply the height and the area.D. Find one third of the product of the heightand area.c. the slant height of the cone if the height of thecone is 12 cmLesson 35-3d. the area of the base if the height and radius areequal81. A wooden paperweight, in the shape of a pyramid,has a base that is an equilateral triangle with a10-cm side and a height of 3 cm. The density of thewood is 0.7 g/cm3.a. What is the volume of the paperweight? Writeyour answer to the nearest tenth of a cubiccentimeter.79. Construct viable arguments. A square isinscribed in a circle with a diameter of 12 cm. Thecircle is used for the base of a cone and the squareis used for the base of a pyramid. The cone andpyramid have the same height, 10 cm.b. What is the mass of the paperweight? Writeyour answer to the nearest tenth of a gram.12 cm10 cm82. Attend to precision. A cone is solid aluminum.The circumference of the cone is 20 cm, the heightis 6 cm, and the mass of the cone is 170 g.a. Before doing any calculations, tell whether thecone or the cylinder has a greater volume.Explain your answer.a. To the nearest hundredth of a centimeter, whatis the radius of the base of the cone?b. To the nearest hundredth of a square centimeter,what is the area of the base of the cone?c. To the nearest tenth of a cubic centimeter, whatis the volume of the cone?b. Calculate the difference in the two volumes.Write your answer as an exact value and as anumber rounded to the nearest tenth.d. To the nearest tenth of a unit, what is thedensity of the aluminum used to make the cone? 2015 College Board. All rights reserved.16SpringBoard Geometry, Unit 5 Practice

Nameclass83. An object has the shape of a prism. Which of thefollowing statements is NOT true?dateLesson 36-186. A cross section of a sphere is a great circle. How isthe surface area of the sphere related to the area ofthe cross section?A. If you know the mass, density, and base area ofthe object, you can calculate its height.B. If you know the base area and height of theobject, you can calculate its density.A. The surface area of the sphere is four times thearea of the cross section.C. If you know the base area, height, and density ofthe object, you can calculate its mass.B. The surface area of the sphere is two times thearea of the cross section.D. If you know the volume and mass of the object,you can calculate its density.C. The surface area of the sphere is p times thearea of the cross section.D. The surface area of the sphere is the square ofthe area of the cross section.84. The mass of a container and its contents is 650 kg.When the container is empty its mass is 75 kg, andthe capacity of the container is 15 m3. What is thedensity of the contents of the container? Write youranswer to the nearest hundredth in units of kg/m3.87. For each radius of a sphere, find the surface area ofthe sphere. Write each answer as an exact value andas a number rounded to the nearest tenth.a. r 5 8 in.b. r 5 20 cm85. Reason quantitatively. Consider Substance Awith a density of 15 kg/m3 and Substance B with adensity of 8 kg/m3.c. r 5d. r 5 0.1 unita. If you take equal masses of the two substancesand mix them, what is the density of themixture?88. Use the formula for the surface area of a sphere.a. Find an exact value for the surface area of asphere if the radius is 7 cm.b. Suppose you mix 20 m3 of Substance A and35 m3 of Substance B. What is the total mass?b. Find an exact value for the radius of a sphere ifthe surface area is 400p cm2.c. What is the total volume of the mixture in Part b?c. Find an exact value for the surface area of asphere if the circumference of the sphere is100p units.d. What is the density of the mixture in Part b?Write your answer to the nearest hundredth. 2015 College Board. All rights reserved.3in.4d. Find an exact value for the circumference of asphere if the surface area of the sphere is 4p cm2.17SpringBoard Geometry, Unit 5 Practice

Nameclass89. Model with mathematics. A solid figure is formedby a cone and two hemispheres. The diameter ofthe hemispheres and the length of the cylinder are12 cm. Find each measure as an exact value.date93. Attend to precision. The volume of a sphere is250 in.3. Find each measure to the nearest tenth.a. the diameterb. the circumference of a great circle12 cm12 cmc. the area of a great circlea. the lateral area of the cylindrical part of the figured. the surface areab. the total surface area of the object94. The number of cubic units in the volume of asphere is equal to the number of square units in thesurface area of the sphere. Which statement aboutthe radius of the sphere is true?90. Make use of structure. The number of squareinches in the surface area of the sphere shown isequal to the number of linear inches in itscircumference. What is the radius of the sphere?A. Its value is p.B. Its value is 3.C. Its value is 1 unit.D. Its value is a measurement less than 1 unit.95. Make use of structure. In the diagram, the radiusof the cone, cylinder, and hemisphere is 3 units.The heights of the cone and cylinder are also 3 units.Lesson 36-291. The volume of a sphere is 100 cm . Find the lengthof its radius to the nearest tenth.rrr3rrra. Find exact values for the volumes of the cone,hemisphere, and cylinder.92. Sphere A has a radius of 8 cm, and a plane throughits center determines two hemispheres. Find anexact value for each measurement.a. the volume of sphere Ab. Use your results from Part a to find the ratio ofthe volume of the cone to the volume of thehemisphere.b. the surface area of sphere Ac. the total surface area of one hemisphere, includingthe cross section determined by the plane 2015 College Board. All rights reserved.18SpringBoard Geometry, Unit 5 Practice

Nameclassc. Use your results from Part a to find the ratio ofthe volume of the hemisphere to the volume ofthe cylinder.98.Reason abstractly. Describe how the term“line” in Euclidean geometry is different fromthe term “line” in spherical geometry.99.The diagram shows a sphere, a great circle, anda dashed object.d. Suppose the radii and heights of the threefigures are r units instead of 3 units.Do you get different results for the ratiovolume of coneand the ratiovolume of hemispherevolume of hemisphere ? Explain.volume of cylindera. Explain why the dashed object and the greatcircle are not parallel lines in sphericalgeometry.Lesson 36-396. Two distinct great circles are drawn on a sphere.Which of the following is NOT a true statement?A. Each great circle determines two hemispheres.b. Show a line on the sphere that isperpendicular to the original great circle.B. The two great circles always form right angleswhere they intersect.C. The two great circles intersect in exactly twopoints.100.D. Each great circle determines a cross section ofthe sphere, and the intersection of the two crosssections is a diameter of the sphere.97.dateConstruct viable arguments. Point A is on agreat circle of the sphere.Suppose that three distinct great circles aredrawn on a sphere. What is the maximumnumber of points of intersection of the threelines?A. 2B. 6C. 8D. 9Lesson 37-1101.AThe surface areas of two cubes are 486 ft2 and864 ft2.a. What are the volumes of the cubes?b. What is the ratio of the volumes of the cubes?c. What is the ratio of the side lengths of thecubes?a. Describe the location of the antipode of point Ain terms of great circles.d. How are your answers to Part b and Part crelated?b. Describe the location of the antipode of point Ain terms of a diameter of the sphere. 2015 College Board. All rights reserved.19SpringBoard Geometry, Unit 5 Practice

Name102.class105.Sphere A has a radius of 6 cm. Sphere B has aradius that is 1.5 times the radius of sphere A.Find the exact values for the following measures.dateWhich of the following statements is NOTcorrect?a. the volume of sphere AA. If the radius of a sphere is doubled, the volumeof the sphere is multiplied by a factor of 8.b. the volume of sphere BB. If the radius of a sphere is tripled, the surfacearea of the sphere is multiplied by a factor of 9.C. If the edge of a cube is multiplied by 4, thevolume of the cube is multiplied by a factorof 64.c. the ratio of the volume of sphere A to thevolume of sphere BD. If the edge of a cube is multiplied by 5, thesurface area of the cube is multiplied by 30.d. the surface areas of sphere A and sphere BLesson 37-2e. the ratio of the surface area of sphere A tothe surface area of sphere B106.Persevere in solving problems. The diagramis a net for cylinder 1.2 cm103.Reason quantitatively

Aug 08, 2016 · SpringBoard Geometry, Unit 5 Practice LeSSon 30-2 6.A triangle has coordinates A(7, 6), B(9, 1), and C(22, 1). What is the area of the triangle? 7.express regularity in repeated reasoning. What is the area of each equilateral triangle? a.side 12 cm b. height 4 3 units c. perimeter 10 in