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Math 12 Applications Outcomes E1, E2, E3, E4, E5 MEASUREMENT (GEOMETRY) EXAMPLES: SECTION 1: PERIMETER (Problems #4-6, 7b, 9, 10) 1. A rectangular beam is to be cut from a log with circular cross section. The beam is to have dimensions 40 cm by 15 cm. a) What is the minimum diameter of a log from which the beam can be cut? b) What is the circumference of the log? 2. Four fluorescent light bulb tubes of diameter 10 cm each are tied together into a bundle with a piece of string, as shown in the diagram of the end view. What is the shortest piece of string required if 10cm of extra string is needed for tying the knot Math 12 Applications Outcomes E1, E2, E3, E4, E5 3. A field 50 m 75 m. needs to be fenced. There must be a fence post in each corner Fence posts must be placed every 2 m at a cost of $2.50 each. Barbed wire is strung horizontally between the posts at three levels as shown in the diagram. The barbed wire fence costs $0.50 per meter. How much will it cost to enclose the field? SECTION 2: AREA (Problems #1-3, 7a, 11-18, 22) 1. The diagram below shows a circular disc with diameter 20 cm with a hole punched out of it. Find the area 20 cm 5cm 2. The diagram shows a pathway with width 3m. If it costs $2.50 /m2 to surface the pathway, what will be the cost? 10 m 15 m Math 12 Applications Outcomes E1, E2, E3, E4, E5 3. A rectangular field has two triangular pieces with hypotenuse length 13m cut off as shown below. Determine the area of the resulting piece of metal. 20m 25 m 13 m 12 m 4. . A pathway around a rectangular lawn is 150 cm wide. The outside dimensions of this garden area are 15 m by 12 m as shown on the diagram below. 15m 12 m pathway It costs $1.50/m2 for the pathway material and $0.85/m2 to seed the lawn. What is the total cost for this garden area? 5. A section of fencing 50 m long surrounds a circular enclosure at a zoo. What is the area of the circular enclosure? Math 12 Applications Outcomes E1, E2, E3, E4, E5 6. A ramp is set up using a rectangular piece of plywood as shown below. a) Determine the area of the plywood. b) Determine the angle of the ramp with the horizontal plywood 0.75 m 2.5m 5m 6. What is the area of an equilateral triangle with each side length 18 cm? Math 12 Applications Outcomes E1, E2, E3, E4, E5 SECTION 3: SURFACE AREA (Problems 19, 21, 23-31) 1. Find the cheapest cost to paint the walls and ceiling of a room with length 8 m, width 6 m and height 3 m. The area of the windows and door is 25m2. Paint can be bought in 1 litre cans which cover 20m2 and cost $8.50 and also in 5 litre cans which cover 100m2 and cost $38.50. 2. A cylindrical can has diameter 18 cm and height 25 cm. a) What is the surface area of the can including the circular top and bottom? b) What is the surface area of the can if the circular top is removed? c) What is the surface area of the can if both the circular top and bottom are removed? 3. . A cylindrical packaging container for sport balls is shown below. The balls have a diameter of 50 cm, and there are 3 balls per package. The company is using material that costs 0.4 cents per square centimeter, how much will is cost to make 10 000 packages? Math 12 Applications Outcomes E1, E2, E3, E4, E5 4. A cube with dimensions 25 cm by 25 cm by 25 cm has a rectangular “hole” punched all the way through it as shown in the diagram below. What is the total surface area of the shape shown below? 20 cm 10 cm 10 cm 20 cm 20 cm 5. What is the surface area of a cone with radius 6 cm and height 12 cm? Math 12 Applications Outcomes E1, E2, E3, E4, E5 SECTION 4: VOLUME (problems #32-48) 1. The diagram shows a section of a flower bed with width 3m and depth 50 cm.. If it costs $12 /m3 for topsoil, what will be the cost? 18 m 16 m 2. What is the volume of a hollow cylindrical pipe with outside diameter 12 cm, thickness 3 cm and length 2.5 m 3. A glass ball with diameter 30 cm is packaged in a cubic box with sides length 50cm. The ball is surrounded by Styrofoam packaging. What is the volume of the packaging? Math 12 Applications Outcomes E1, E2, E3, E4, E5 4. A sphere with diameter 12 cm is dropped into a cylinder with diameter 20 cm and height 30 cm. If the cylinder is half full of water, how far does the water level in the cylinder rise? SECTION 5 RATES 1. A cylindrical fuel tank is being filled at the rate of 150 L/minute. The diameter of the cylinder 6 m and the height is 2 m. 1 L = 1000 ml a) How high will the fuel level be after 1 hour? b) How long would it take to fill the tank? 2. A cylindrical fuel tank with diameter 6 m and height 5 m can be filled in 2 hours. What is the filling rate in litres per minute? 1 L = 1000 ml