Mathematical Reasoning,Lesson 48 Pyramids Cones and Spheres. The purpose of the GED test is to provide students with the skills necessary to either further their education or. be ready for the demands of today s careers, Lesson 48 Warm up Solve the Lake Superior Questions Time 5 10 Minutes. Write on the board Lake Superior is located between Canada and the U S There are about. 175 000 Canadians living along the lake s northern border and about 425 000 Americans. along its southern border,Basic Questions, What is the ratio of Canadians to Americans living along Lake Superior. 425 000 17, Americans consist of what percent of those living along Lake Superior. 425 000 425,Extension Question, The volume of water in Lake Superior is 3 0 x 1015 gallons Write this number in standard form. o 3 000 000 000 000 000 3 quadrillion gallons, o Note This enough water to cover all of South and North America in one foot of water. Lesson 48 Activity 1 Volume and Surface Area of a Sphere Time 15 Minutes. 1 Use the attached Notes pages 22 26 for reference. 2 A sphere is a round figure with no bases or faces a ball is a good example. 3 The formulas for volume and surface area of a sphere are similar to each other See below. 4 Solve the volume and SA of the spheres on Worksheet 48 1 Do 1 and 9 as examples If the. diameter is given it must be divided by two to get the radius. 5 Students can do some of the problems in class and complete the rest for homework. D Legault Minnesota Literacy Council 2014 2,Mathematical Reasoning. Lesson 48 Pyramids Cones and Spheres, Lesson 48 Activity 2 Volume of Pyramids and Cones Time 20 Minutes. 1 The objective of this activity is to find the volume of cones and pyramids. 2 These two are grouped together because their formulas are similar For both the volume. 1 3 area of base x height, 3 A cone is a solid 3 dimensional object with a circular base and one vertex point A good. example is an ice cream cone without the ice cream in it. 4 Since a cone has a circle as the base we use 1 3 times r2 for the area of the base and. multiply it by the height, 5 A pyramid is a solid 3 dimensional object with a polygon base and triangular sides that meet. at an apex point A pyramid can be a square pyramid a triangular pyramid a pentagonal. pyramid etc, 6 The formula for the volume of a pyramid is 1 3 B the area of its base multiplied by its height. 7 Do 1 and 2 on Worksheet 48 2 as examples Then students can do the rest on their own. 8 Volunteers can do a few problems on the board, Lesson 48 Activity 3 Surface Area of Pyramids and Cones Time 20 Minutes. 1 The objective of this activity is to calculate the SA of pyramids and cones. 2 The lateral area as referred to in videos and worksheets means the sum of the area of all. surfaces except for the top and bottom bases, 3 The slant height referred to as s or l on videos or worksheets is the height of the face or the. height of the triangles on the pyramid The s is used on the GED formula sheet. 4 Finding the surface area of the pyramid means finding the area of each triangle and adding. the area of the base, 5 Use 10 on Worksheet 48 3 as an example Have the students find the area of one triangle. multiply it by 4 and add the area of the base They should get 4 6 3 4 16 66 4. 6 The formula given on the GED test gets the same results and is a little shorter but it is. important for students to understand what they are doing when they calculate the surface. 7 The SA of a cone is r s r2 multiplied by the radius by the slant height of the cone the. area of the circular base, 8 Use 1 on Worksheet 48 3 as an example The radius is 13 and the slant height is 30 Using the. formula we get 3 14 13 30 3 14 132 1224 6 530 66 1755 26 units2. 9 Questions 1 6 on the worksheet are meant to label the parts of the figures correctly and. questions 7 12 are to solve You can have students solve all of them for SA if you have time. 10 Have volunteers do 1 2 problems on the board,D Legault Minnesota Literacy Council 2014 3. Mathematical Reasoning,Lesson 48 Pyramids Cones and Spheres. Lesson 48 Activity 4 Word Problems Time 45 Minutes. 1 Do the problems on pages 108 109 of the student book together. 2 Have students do the problems in the workbook pages 154 157 independently. 3 Volunteers can solve a few of the more challenging problems on the board. Lesson 48 Application Guatemalan Sinkhole Time 15 Minutes. 1 Become familiar with the activity before class, 2 Show the students the photo of the sinkhole which will foster good discussion. 3 Follow the suggested format of asking questions and discussion as time permits. 4 The purpose of an activity such as this one is for students to see there are real life applications. of the formulas and to make it interesting,D Legault Minnesota Literacy Council 2014 4. V Ah pr h p 6 10 360p cubic inches An approximation of. radius of this exact answer would be 1130 97336 cubic inches. circle Mathematical Reasoning,the number,Lesson 48 Pyramids Cones and Spheres. Lesson 48 Notes on Spheres Cones and Pyramids, Our next set of formulas is going to be for spheres A sphere is most easily. thought of as a ball The official definition of a sphere is a three. dimensional surface all points of which are equidistant from a fixed point. called the center of the sphere A circle that runs along the surface of a. sphere to that it cuts the sphere into two equal halves is called a great great circle. circle of that sphere A great circle of a sphere would have a diameter that of a sphere. is equal to the diameter of the sphere,Surface Area of a Sphere. r the radius of the sphere,the number that is approximated by 3 141593. Volume of a Sphere,r the radius of the sphere,the number that is approximated by 3 141593. D Legault Minnesota Literacy Council 2014 5,Mathematical Reasoning. Geometry Notes,Lesson 48 Pyramids Cones and Spheres. Volume and Surface Area Page 23 of 57, Find the volume and surface area of the figure below. This is a sphere We are given that the diameter of the sphere is. 3 inches We need to calculate the radius of the sphere to. calculate the volume and surface area The radius of a sphere is. half of its diameter This means that the radius is. 1 1 5 1 29 29,r d 3 1 8125 inches We can now just,2 2 8 2 8 16. plug this number in to the formulas to calculate the volume and. surface area,Volume V pr 3 p 1 8125 3 24 941505 cubic inches. Surface Area SA 4pr 2 4p 1 8125 2 41 28219 square inches. Find the volume of the figure,Volume of a,Solid with a 5. atching Base,area of the,e of the solid 13,height of the. D Legault Minnesota Literacy Council 2014 6,pezoid Area of the trapezoidal base. the height of 1 1, trapezoid A b1 b2 h 13 8 5 52 5 square units Mathematical Reasoning. Volume of trapezoidal solid,52 Pyramids,5 15 787Cones. 5 cubicand Spheres, Our next formulas will be for finding the volume of a cone or a pyramid. These two formulas are grouped together since they are very similar Each. is basically 1 3 times the area of the base of the solid times the height of. the solid In the case of the cone the base is a circle In the case of the. pyramid we will have a base that is a rectangle The height in both cases is. the perpendicular distance from the apex to the plane which contains the. A pyramid is a solid figure with a polygonal base in our case a rectangle and pyramid. triangular faces that meet at a common point the apex A cone is the. surface of a conic solid whose base is a circle This is more easily thought of cone. as a pointed ice cream cone whose top is circular and level. Volume of a Rectangular Pyramid,l the length of the base of the pyramid. w the width of the base of the pyramid,h the perpendicular height of the pyramid. D Legault Minnesota Literacy Council 2014 7,Mathematical Reasoning. Geometry Notes,Lesson Area, Volume and Surface 48 Pyramids Cones and Spheres Page 25 of 57. Volume of a Cone,r the radius of the circular base of the cone. the number that is approximated by 3 141593,h the perpendicular height of the cone. Find the volume of the figure, Since the figure has a circular base and looks like an ice cream. cone this must be a cone In order to find the volume of a cone. we need the radius of the circular base and the height. perpendicular height of the cone The height is given as 12. centimeters The other measurement of 10 centimeters is the. diameter of the circular base We thus must calculate the radius. to get r d 10 5 centimeters We are now ready to plug. into the volume of a cone formula V,p 52 12 100p, cubic centimeters is the exact volume An approximation of this. volume would be 314 159266 cubic centimeters,D Legault Minnesota Literacy Council 2014 8. Mathematical Reasoning,Lesson 48 Pyramids Notes,Cones and Spheres. Volume and Surface Area Page 26 of 57,Find the volume of the figure. The base of this figure is a rectangle and the sides of the figure. are triangles thus this figure is a rectangular pyramid The height. perpendicular height is 10 inches The length of the base is 7. inches and the width of the base is 5 inches Since we have all of. the parts for the volume formula we can just plug into the volume. of a rctangular pyramid formula to get,V lwh 7 5 10 cubic inches An approximation of. this volume would be 116 66667 cubic inches, Just like with areas we can add and subtract volumes of different solids to. find the volume of a solid that is a combination of more than one solid or. that have one solid removed from another,Find the volume of the figure. D Legault Minnesota Literacy Council 2014 9,Mathematical Reasoning. Lesson 48 Pyramids Cones and Spheres,Worksheet 48 1 Spheres. D Legault Minnesota Literacy Council 2014 10,Mathematical Reasoning. Lesson 48 Pyramids Cones and Spheres,D Legault Minnesota Literacy Council 2014 11. Mathematical Reasoning,Lesson 48 Pyramids Cones and Spheres. Worksheet 48 1 Answers,D Legault Minnesota Literacy Council 2014 12. Mathematical Reasoning,Lesson 48 Pyramids Cones and Spheres. D Legault Minnesota Literacy Council 2014 13,Mathematical Reasoning. Lesson 48 Pyramids Cones and Spheres,Worksheet 48 2 Volume of Pyramids and Cones. D Legault Minnesota Literacy Council 2014 14,Mathematical Reasoning. Lesson 48 Pyramids Cones and Spheres,Worksheet 48 2 Answers.

LESSON 48: Pyramids, Cones, and Spheres Lesson Summary: For the warm up, students will solve a problem about Lake Superior. In Activity 1, they will calculate the volume and surface area of spheres. In Activity 2, students will calculate the volume of pyramids and cones. In Activity 3, students they solve for the surface area of pyramids and ...

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