Year 8 Maths Well Above Level – Measurement Extension 1. Application Questions Learning Intention: to be able to apply measurement formulae to all different kinds of shapes, relating to perimeter, area and volume Success Criteria: provide clear working in solving application problems. Complete the following questions in your workbook, show full working out for each question. 8.3 Q24 8.4 Q23, 28 8.5 Q16 8.7 Q13 16 2. Problem Solving Learning Intention: to be able to identify a successful problem-solving strategy and use it to solve a problem. Success Criteria: provide clear and systematic working in the solution of the problem. GRAZING COW A cow is tethered by a piece of rope 50m long. The rope is fastened to a hook located 10m from the corner of the longest side of a barn measuring 60m x 30m. What area of ground around the barn can the cow graze? ( answer correct to 2 decimal places) OVERLAPPING SQUARE . Two overlapping squares, QTVU and SXYZ, are drawn inside the rectangle PQRS so that the perimeters of the three shaded rectangles are equal. If the lengths of the sides PQRS are 20cm and 22cm, what is the sum of the perimeters, in centimetres, of the squares QTVU and SXYZ? ROPING LOGS Six Logs have been loaded on a truck. If each log had a diameter of 60 cm, what is the length of the rope which binds them (excluding the length which is needed for the tying). In answering this, show and explain all workings. The Fence Problem A new fence is required to be constructed on three sides of a rectangular property. The property measures 45m x 30m and the fence will cover only one of the 30m sides. The fence will consist of three rails, a kick board, posts and palings. (you may need to purchase more palings than you require) CLEARLY SHOW ALL WORKING AND STATE WHAT YOU ARE TRYING TO FIND 1. What length of timber is required for the kick board? 2. If the kickboard timber costs $1.90 per metre, what is the cost of the kickboard? 3. If the railing timber costs $2.25 per meter, what will be the total cost of timber for the railings? 4. i) How many posts will be needed if the posts are to be 5m apart where each corner or straight edge has one post? (show clearly how you worked this out, a diagram may help) ii) Find a general rule using ‘n’ to work out how many posts you need. Hint: Break this problem down and look for a pattern 5. If the post timber costs $13.65 per post, what is the cost of the posts? 6. The palings are 9cm wide and cost $1.05 each. If the minimum number of are used to guarantee privacy, how many palings would you have to buy and their cost? (assume they do not overlap) 7. What is the total cost of the fence? (include a table to show each section’s cost then the total cost) palings what is 8. A modification has been suggested by a friend. The problem is the palings will probably shrink as the years go by and therefore the privacy be partially lost. It is recommended to nail the palings to the posts with a 15mm overlap. will a. Develop a formula for the total length L of the fence in terms of number of palings n. (you must show how you arrived at your formula) the b. Use your formula to calculate the number of palings required to complete the fence. If you can’t work out a formula find another way to solve this problem. If you set it out like the table below it may help you find a pattern. Number of palings n 1 2 3 4 5 n Total length L (mm) Simplification 3. Year 9 Measurement – Oxford Maths 9 Ex 6A Check in with your teacher then answer the following questions from Oxford Maths 9 Ex 6B Check in with your teacher then answer the following questions from Oxford Maths 9 Ex 6C Check in with your teacher then answer the following questions from Oxford Maths 9 Ex 6D Check in with your teacher then answer the following questions from Oxford Maths 9 Checkpoint – all questions Let your teacher know you are ready for an assessment 😊