40 h = 7. Work : (example) Length of BD and OD. m OB = = m OD = 4. Length of OB Since BOD is a right triangle

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1 Mathematics 06/6 REVIEW 6 1- ontents Question Item Objective Type Skill LG.04 Extended answer Problem solving 01 GEO.04 Extended answer Problem solving 054 GEO.04 Extended answer Problem solving 4 06 LG.04 Extended answer Problem solving 5 00 GEO.0 Extended answer Problem solving 6 06 GEO.04 Extended answer Problem solving GEO.04 Extended answer Problem solving GEO.04 Extended answer Problem solving GEO.04 Extended answer Problem solving GEO.04 Extended answer Problem solving GEO.04 Extended answer Problem solving GEO.04 Extended answer Problem solving GEO.04 Extended answer Problem solving - orrection key 1 : (example) Length of D and OD m 8 m D = = = 4 m OD = 4 F Length of O Since OD is a right triangle m O = (m OD) m O = = m O = (m D) Length of Since O is a right triangle m = (m O) + (m O) 8 cm O D 4 cm 4 cm m = m = Length of F 1 + ( ) m 1.7 m F = = 6.6 Length of path F Result Length of F = m F + m = 14.6 The ant must cover a distance of 14.. : (example) rea of the roof (10 0) = 400 m rea of the gables m rea of the sides = Total surface area = 80 Height h of the openings (0 h) = h = 40 h = 7 Result The height of each opening is 7 metres.

2 Example of an appropriate solution Height of pyramid (h 1 ) h Volume of pyramid base h Volume of prism = 4. Height of prism (h ) h1 8. V = base h 4. h 1 1 h Height of box (h) h = h 1 + h h h 9.16 nswer The total height of the box is : (example) Length of Hillside Road between Simcoe venue and Elm Street m m m m m m West Simcoe venue School Elm street East m m m m Hillside Road Marie and lex's House m 00 Distance walked by lex on Hillside Road 00 0 = 80 Total distance walked by lex = 40 Total distance walked by Marie = 80 Difference between these two distances = 40 nswer lex's route is 40 m longer than Marie's. 5 Example of an appropriate solution The pyramid has a triangular base Measure of the edges m S = m S = m S =16 Measure of the angles m S = m S = m S = 90 because S is a vertex of the cube rea of the base of the pyramid Height of the pyramid S is the height and measures 1 Volume of area of base h rea of base h S nswer The volume of the pyramid is 68.7 cm.

3 The volume of the silo. r h = m The volume of the four silos is m The volume of the space between the silos (4 4 r )10 = = 4.4 m The total volume available to the farmer = m The wheat required by the farmer for one year = m Result The supply is not sufficient. ny other complete and acceptable work with the correct result The volume of a cone : The volume of 1 cones : = The height of the pudding : The depth of the saucepan : = 14.5 Result The depth of the saucepan is 14.5 cm. ny other complete and acceptable work with the correct result. Volume of the cylinder in cm V = rea of base height V = 4 V = 50.4 ( =.14) 50.7 (using π on calculator) Volume of the hemisphere in cm V = V = 4 r V = ( =.14) (using π on calculator) Volume of the rectangular prism in cm V = rea of base height V = V = 88 mount of transparent plastic in cm 88 ( ) = 1.01 ( =.14) 88 ( ) = 0.97 (using π on calculator) Result The amount of clear plastic is about 1 cm. : (example) Radius of the cone 8.66 = 4. cm Height of the cone 7.4 Volume of the cone 4. r h V = cm Total volume of the cup 15 ml or 15 cm Volume of the cylinder 15 cm cm = 7. Radius of the cylinder 1 cm = 0.5 cm Height of the cylinder V = r h h cm Result The height of the cylindrical part is 9.4 cm. Note : ccept answers in the interval [9.1, 9.].

4 10 Width of rectangle E = 8 Measure of rd side of triangle D rea of base of solid b = 8 6 = 4 10 cm Volume of solid V = b h V = 4 15 = 60 E 15 cm nswer The volume of this solid is 60 cm. 11 Measure of the side of the cube 6c = 600 c = 10 Measure of the (apothem) slant height of the pyramid + a = 10 5 a = 15 a cm a Total surface area of the pyramid b = = 100 l = l Perimeter of the base (apothem) slant height =.6 t = b + l t t.6 nswer: The total surface area of the pyramid is.. n answer in [, 4] is acceptable. 5 cm 1 Example of an appropriate solution Glass Ice cube 15 cm cm Volume of glass V v = r h V v = () 15 V v Volume of liquid 55 ml = 55 cm Volume available for the ice cm 55 cm cm Volume of ice cube V c = c V c = V c = 7 Number of ice cubes nswer =.56, therefore cubes Simon can add ice cubes.

5 1 Example of an appropriate solution rea of the base (6 6) + (.14 9) = 64. Volume of the container = cm Quantity of liquid 4 cans ( cans of water + 1 can of concentrate) 4 00 ml = 100 ml onversion of the measures cm = ml nswer: No, because the container is missing 4 ml of space. Note Using on the calculator = cm V = cm.

6 Mathematics 06/6 REVIEW 6 1 The adjacent right pyramid has a square base with side 8 cm. Height O is 1 cm. n ant sits at point F midway between and. ait has been put at. If the ant takes path F to get to the bait, what distance must it cover? F O D 4 cm 4 cm 8 cm Give your answer to the nearest centimetre. Result : The ant must cover a distance of cm. It takes 776 m of building material to cover the exterior surface of an airplane hangar completely. The hangar has two identical openings, one at each end. Each gable above the opening is 6 metres high. The dimensions of the hangar are shown below. 10 m 10 m 6 m h h 0 m 16 m What is the height h of each opening of this hangar? Result : The height of the openings is. box, in the shape of a square-based prism topped by a right pyramid, has a volume of 78 cm. Its dimensions are indicated on the figure to the right. What is the total height of this box? 8. 1 cm nswer : The total height of the box is cm.

7 4 Marie and her brother lex take different routes to get to school. Marie walks 0 m west along Hillside Road, turns right on Simcoe venue and then walks 160 m. lex walks east along Hillside Road, turns left on Elm Street and then walks 40 m. School Note: The figure is not drawn to scale. West Simcoe venue Elm Street East lex's route is longer than Marie's. How many metres longer is it? Hillside Road Marie and lex's House nswer lex's route is m longer than Marie's. 5 Each edge of a wooden cube is 4 cm in length. This cube is cut into two pieces. The cut is made through the three points, and, each of which is 1 away from vertex S of the cube. What is the volume of the pyramid that is formed? S nswer : The volume of the pyramid is cm. 6 farmer intends to store his wheat in four cylindrical silos each 10 m high and 4 m in diameter. When the silos are filled, the wheat accumulates between them as indicated in the view of silos from above. View of silos from above View of silos in perspective Space between silos To feed his animals the farmer needs 1.5 m of wheat per day. If the silos and the space between them are filled to capacity, will the farmer have enough wheat for 65 days? (Use.14 for.)

8 7 pudding was prepared in a saucepan of radius 10 cm. The pudding filled 1 cones of the shape and dimensions shown below. 10 cm cm 8 cm Space above the pudding ONE SUEPN What was the depth of the saucepan if cm of space had to be left above the pudding so that it did not spill during the cooking process? Result : The depth of the saucepan is cm. 8 The paper-clip holder shown below is in the shape of a right prism. avity lock of clear plastic r cm 8 cm 4 cm cm r cm How much clear plastic is there in the paper-clip holder? Round your answer to the nearest whole number. Result : The amount of clear plastic is about cm. 9 The following is a cross section of a cone-shaped cup mounted on a right cylinder. When the cone and the cylinder are completely filled with liquid, the total capacity of the cup is 15 ml. The apothem of the cone is 7.4 cm, the diameter of the cone is 8.6 and the diameter of the cylinder is 1 cm cm h Taking into account the measurements given and assuming the cone to be complete (not reduced) find the height of the cylindrical part. (Notes : 1 cm = 1 ml and =.14). Show your work.

9 10 The net of a solid is shown on the right. The width of rectangle D is 10 cm. The length of rectangle E is 15 cm and its area is 10 cm. D What is the volume of the solid once it has been built? 10 cm E 15 cm nswer The volume of this solid is cm. 11 The figure to the right shows a pyramid within a cube. The total surface area of the cube is 600 cm. Vertex S of the pyramid is at the centre of the top face of the cube. Find the total surface area of the pyramid after it is removed from the cube.. S nswer: The total surface area of this pyramid is cm. 1 Simon emptied the contents of a soft drink can into a cylindrical glass. The glass has a diameter of and a height of 15 cm, as illustrated in the diagram below. soft drink can holds 55 ml of liquid. He wants to put some ice cubes, whose sides measure cm, into the glass. Glass Ice cube 15 cm cm What is the maximum number of ice cubes that Simon can add to the drink in the glass, without it overflowing?

10 1 To make orange juice, one can of concentrate must be mixed with cans of water, each with a capacity of 00 ml. The juice will be mixed in a container 18 cm high. The top of the juice container is a square bounded by semicircles, each with a radius of cm, as shown. r 18 cm Front view Is the container large enough to hold all the juice? Why or why not? Show your work. (Round your final answer to the nearest ml.) nswer: Yes, because the container has ml of space left. or No, because the container is missing ml of space.