Learning Outcome 4 Measurement

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1 Maths in Context Learning Outcome 4 Measurement Exercise Book

2 Learning Outcome 4 Exercise 1 Select the most appropriate metric units for measuring each item. 1. The height of a person: (A) mm (B) cm (c) m 2. The mass of an egg: (A) kg (B) mg (C) g 3. The capacity of a car engine: (A) L (B) ml (C) kl 4. The speed of a train: (A) m/s (B) m/h (C) km/h 5. The length of a soccer field: (A) km (B) m (C) cm 6. The mass of a rhinoceros: (A) t (B) kg (C) mg 7. The capacity of a swimming pool: (A) L (B) kl (C) ml 8. The energy contained in a muesli bar: (A) J (B) MJ (C) kj 9. The time taken to write your signature: (A) s (B) min (C) h Select the most appropriate measurement for each item. 10. The length of your index finger: (A) 7 cm (B) 7 mm (C) 7 m 11. The mass of an apple: (A) 220 mg (B) 220 kg (C) 220g 12. The capacity of a small fish tank: (A) 36 kl (B) 36 L (C) 36 ml 13. Average walking speed of a person: (A) 40 km/h (B) 4 km/h (C) 4 m/min 14. The length of a football field: (A) 100 m (B) 100 km (C) 100 cm 15. The mass of a car: (A) 1200 t (B) 1200 kg (C) 1200 mg 16. The average dose of a medicine: (A) 10 L (B) 10 µl (C) 10 ml 17. The height of a three-storey building: (A) 1000 m (B) 100 cm (C) 10 m 18. The total mass of ten boys: (A) 500 kg (B) 50 kg (C) 5 mg Learning Outcome 4 Exercise 2 Convert the following measurements to the units shown: mm = cm g = kg mm = cm cm = m cm = m mm = m mm = m m = km m = km 9. 8 cm = mm cm = mm m = mm m = mm m = mm m = cm m = cm µm = mm µm = m km = cm km = mm km = mm g = kg g = kg kg = g kg = g kg = t kg = t kg = t t = kg t = g ml = L ml = L L = ml L = ml kl = L kl = L L = kl L = kl kl = ml ml = kl

3 Learning Outcome 4 Exercise 3 State the number of significant figures in each of these measurements: cm kg mm L cm g km Complete the table below (the first one is done for you): Measurement Absolute error Lower limit Upper limit 8. 4 cm 0.5 cm 3.5 cm 4.5 cm 9. 7 cm cm kg g L ml Complete the table below (the first one is done for you): Measurement Absolute error mm 0.5 mm kg ml m cm g Relative error = or Percentage error = 10% Learning Outcome 4 Exercise 4 1. Calculate the perimeter of the rectangles whose dimensions are given. Note: the dimensions of a rectangle are its length and width. Length, L cm Width, W cm Perimeter, P cm (a) 3 2 (b) 6 5 (c) 10 1 (d) Calculate the perimeter of the squares with side lengths (a) 2 mm (b) 5 m (c) 10 km (d) 7.5 cm

4 3. The perimeter of a rectangle is 20 cm. (a) If the length is 6 cm, what is the width? (b) If the length is 8 cm, what is the width? (c) If the width is 1 cm, what is the length? 4. (a) A square has a perimeter of 20 cm. What is the length of each side? (b) A square has a perimeter of 100 m. What is the side length of the square? 5. Draw three rectangles that have a perimeter of 12 cm. Learning Outcome 4 Exercise 5 1. An equilateral triangle is a triangle with three sides equal. Find the perimeter of the equilateral triangles shown below. (a) (b) 5 cm 5 cm 2 m 2 m 5 cm 2. An isosceles triangle is a triangle with two of its sides equal in length. (a) Find the perimeter of an isosceles triangle with sides measuring 8 mm, 8 mm and 10 mm. (b) Find the perimeter of the triangle below: 2 m 26 m 26 m Learning Outcome 4 Exercise 6 48 m Find the length of the side marked x in each of the following x cm 3. 6 m x m x mm 9 mm 20 cm 14 cm 8 m 10 mm 4. A square ABCD, shown below, has side lengths 6 cm. Find the length of the diagonal, AC. Give the answer correct to one decimal place. A B D C In each of the following questions, draw a diagram showing the given information, and then find the required lengths. 5. The width of a rectangle is 9 m and its diagonal is 15 m. Find the length of the other side of the rectangle.

5 6. A ladder that is 2.6 metres long is leaning against a wall. The foot of the ladder is 1 metre from the base of the wall. How far up the wall does the ladder reach? (Assume that the wall is at right angles to the ground). 7. Find the perimeter of these triangles: (a) (b) 9 m 18 cm 12 m 24 cm 8. Find the perimeter of ABC below, given AB = AC = 65 cm and AD = 25 cm. A B C Learning Outcome 4 Exercise 7 D Find the circumference of the following circles, giving the answer correct to two decimal places: 1. Diameter 10 cm 2. Diameter 8.4 cm 3. Diameter 26 mm 4. Radius 5 cm 5. Radius 10 cm 6. Radius mm Find the perimeter of the following figures, giving the answer correct to two decimal places: 7. 5 mm 12 mm Hint: the perimeter is the distance around the outside of the figure, so P = Half the circumference of a circle with diameter 12 mm. P = (0.5 π 12). Find this using your calculator m 28 cm 7 m 24 cm Hint: use Pythagoras Theorem to find the length of the sides of the triangle.

6 10. Find the difference between the circumferences of the two concentric circles below (concentric circles are circles that have the same centre). The smaller circle has a radius of 1 cm, and the larger circle has a radius of 2 cm.

7 Learning Outcome 4 Exercise 8 Area formulae: Rectangle: A = LB Square: A = s 2 Triangle: A = 2 1 bh Circle: A = πr 2 Find the area of these shapes. For circles, give the answer correct to two decimal places mm 5 cm 8 m 4.2 mm 12 cm m 7 cm 7.8 m 8.4 cm 23 mm m 8.5 m 9.4 mm 8.3 mm Answer these questions. 9. The area of a square is 81 cm 2. What is the side length of the square? 10. The area of a rectangle is 56 mm 2. If the length is 8 mm, what is the width? 11. The area of a triangle is 24 m 2. If the base of the triangle is 12 m, what is the height of the triangle? 12. The area of a circle is 100 cm 2. Find the radius, correct to 2 decimal places. [Hint: π r 2 = 100, so r 2 = 100 π. Then r = ( 100 π). Use your calculator.]

8 Learning Outcome 4 Exercise 9 Find the area of these shapes mm 5 mm 7.5 cm 6 cm 12 mm 11 cm cm 12 m 6 cm 24 m 5. Find the shaded area of the figure below, given that the square has a side length of 16 cm, and the radius of each of the circles is 4 cm. 6. Find the shaded area, if the rectangle measures 6 cm by 8 cm, and the diameter of the circle is 10 cm. Learning Outcome 4 Exercise Find the volume of a prism with (a) Area of the base 10 cm 2, height 5 cm (b) A = 3.45 m 2, H = 0.4 m (c) A = 17.5 cm, H = 12 mm [Hint: change the height to cm first] 2. Find the volume of a cube with edge length (a) 2 cm (b) 4 mm (c) 5 m. 3. Find the volume of a rectangular prism with (a) Length 12 cm, Breadth 4 cm, Height 10 cm (b) L = 4.25 m, B = 4 m, H = 2.5 m (c) L = 25 cm, B = 10 cm, H = 35 mm [Hint: change the height to cm first] 4. Find the volume of a cylinder (or circular prism) with (a) base radius 6 m and height 8 m (b) r = 12.8 cm, h = 10 cm (c) r = 0.3 m, h = 60 cm [Hint: change the height to m first]

9 5. Find the volume of these prisms: (a) (b) (c) 3 m 6 cm 18 cm 4 m 8 cm 3 cm Area of base triangle is 14.8 cm 2 3 m 6. Find the volume of these prisms: (a) (b) 4 cm L = 2 m, B = 0.5 m, H = 0.6 m 11 cm Learning Outcome 4 Exercise 11 Find the volume of these pyramids: cm 12 mm 4 cm 4 cm 8 mm 3. Base rectangle measures 4. Base triangle has area 10 cm mm by 9 mm. Height of pyramid is 6.6 cm. Height of pyramid is 14 mm. Learning Outcome 4 Exercise 12 Find the volume of a sphere with radius 1. 1 m 2. 5 cm cm

10 Learning Outcome 4 Exercise 13 Find the volume of these 3-D shapes m 6 m 6 cm 7 cm 4 cm 6 cm 10 cm m 6 m 2.4 m 2 m 3 m 2 m 3.6 m 4.8 m 2.2 m Next Learning Outcome 4 Exercise Find the capacity of a cylindrical container with base radius 3 cm and height 13.5 cm. 2. Find how many litres of water are needed to fill a fish tank that is in the shape of a rectangular prism, if the dimensions of the tank are 40 cm by 28 cm by 30 cm. 3. A water storage tank is built in the shape of a rectangular prism. It is 9.9 m long, 6.1 m wide and 1.4 m deep. Find: (a) the volume of the tank (b) the capacity of the tank in kilolitres (c) the mass of water in the tank if 1 kilolitre of water weighs 1 tonne. 4. The tipper of a truck is a rectangular prism in shape. It is 6.5 m long, 3.1 m wide and 1.4 m high. (a) Calculate the volume of the tipper (b) If the truck carries sand, and 1 m 3 of sand weighs 1.6 tonnes, find the weight of sand carried when the truck is three-quarters full. 5. A farmer bought a 200 litre drum of petrol. If the petrol cost 95.6 cents per litre, how much did the drum of petrol cost? 6. Jack filled his car up with petrol at the petrol station. If he paid $45 for the petrol, and the price of the petrol was $0.98/L, how many litres of petrol did Jack buy?

11 Learning Outcome 4 Exercise A gate 860 mm by 1250 mm is to have a diagonal timber brace fitted to give it strength. To what length should the timber be cut, to the nearest millimetre? 2. A rectangular block of land is 18 m by 48 m. (a) Find its perimeter. (b) Find the cost of fencing the land at $24 per metre. (c) Find its area. (d) Find the cost of laying turf on the whole block, if turf costs $1.75/ m Freda is going to make three circular cushions with diameter 35 cm. She is going to trim the edge of each one with lace. If she allows 10 cm extra for each cushion, how much lace will she need to buy, to the nearest centimetre? 4. A square sandpit has an area of 4.41 m 2. (a) How long is each side? (b) If the sandpit is to have wooden logs around its edge, how much timber is required? (c) If the sandpit is to be filled to a depth of 30 cm with sand, how many cubic metres of sand will be needed? 5. Jack is planning to erect a garden shed on a concrete slab. The slab is to be 3000 mm by 4000 mm by 100 mm. (a) How many cubic metres of concrete would be needed for the slab? (b) What will be the cost of the concrete if it costs $135 per cubic metre? 6. Steve is planning to paint the walls and ceiling of his shop. The room is 15 m long, 9 m wide and 2.7 m high. The doors and windows have a combined area of 12.5 m 2. (a) Calculate the area to be painted (b) How much paint will he need for 2 coats if 4 L of paint covers an area of 65 m 2? (c) Cans of paint cost $49.95 for 4 L. How much will the paint cost? 7. The largest pyramid in Egypt is The Great Pyramid of Cheops (or Khufu). It has a square base of side 230 m and a perpendicular height of 137 m. (a) What is the volume of the pyramid, to the nearest cubic metre? (b) If The Great Pyramid of Egypt contains stone blocks, each weighing approximately 2.45 t, what is the total mass of the pyramid, in megatonnes? 8. A small wheat silo is in the shape of a cylinder with a base diameter of 5 m and a height of 7.5 m. What volume of wheat does it hold, to the nearest m 3? 9. Jane buys oats for her horse in 20 kg sacks. If she feeds her horse 650 g of oats each day, how long will the sack of oats last? 10. Each tablet in a bottle contains 250 mg of Vitamin C. (a) What is the total amount of vitamin C, in grams, needed to produce a bottle of 100 tablets? (b) If you took one tablet each day for 2 weeks, how many grams of Vitamin C would you have consumed? Learning Outcome 4 Exercise The recommended daily intake of calcium for teenagers is 1.2 g per day. If reduced fat milk contains 125 mg of calcium per 100 ml, how much milk would a teenager need to drink per day if that was the only source of calcium? 2. Don received a water bill. He had used 81 kl over a three-month period. (a) If the Water Board charges 68 cents per kilolitre, how much was the water bill? (b) What was Don s average water consumption per month? (c) Estimate the amount of water Don would use in a year. (d) Calculate Don s average daily usage in litres (to the nearest litre). 3. Electrical appliances generally show their wattage rating, which is the amount of energy the appliance uses in one hour when it is operated continuously. For example, a 60 watt appliance uses 60 watts of energy in one hour. Electricity consumption is usually measured in kilowatt hours (kwh). The charge rates for an electricity company are cents per kwh. Calculate the electricity bill for a family that uses 2850 kwh. 4. The recommended pressure for car tyres is about 220 kilopascals (kpa). When Bill tested the pressure in his front passenger side tyre, it measured 198 kpa. How many kpa is this below the recommended pressure?

12 5. The length of mainland Australia s coastline is approximately m. (a) How many kilometres is this? (b) How long would it take to walk around the coastline, if you walked at an average speed of 5 km/h for an average of ten hours per day? 6. The Earth is approximately spherical in shape, with a radius of approximately 6400 km. (a) Find the distance around the Earth along the Equator, to the nearest kilometre. (b) Find the volume of the Earth, in km 3, correct to 2 significant figures. (c) The Moon has a diameter of approximately 3600 km. Find the volume of the Moon, in km 3, correct to 2 significant figures. (d) Find how many times greater the volume of the Earth is, compared to the volume of the Moon. Answer to the nearest whole number. 7. If the volume of a cube is 1000 cm 3, what is the side length of the cube? 8. Builders usually measure in millimetres and carpet layers quote by the square metre. (a) How many square metres of carpet will be needed for a room measuring 3500 mm by 4500 mm, to the nearest metre. (b) Find the cost of carpeting the room, if carpet costs $95 per square metre? 9. The engine capacity of a car is the total volume of the cylinders, in litres. (a) Calculate the engine capacity (in litres) of a 4-cylinder car if each cylinder has a diameter of 6.9 cm and a height of 10.7 cm. (b) A V8 Holden has eight cylinders, each with diameter 8 cm and depth 10 cm. What is the capacity of the engine? Answer to 4 significant figures. 10. Ben needed to calculate the capacity of the cylindrical rainwater tank attached to his house. He took these measurements: circumference 6.6 m and height 2.8 m. (a) Calculate the radius of the base of the tank, to three significant figures. (b) Calculate the capacity of the tank, to the nearest litre. This Conclude Learning Outcome 4 Make sure you have ticked each box in your online Exercise Summary Page

MA 40S APPLIED UNIT F: DESIGN AND MEASUREMENT CLASS NOTES

1 MA 40S APPLIED UNIT F: DESIGN AND MEASUREMENT CLASS NOTES 1. Introduction. In Grade 1 Applied you learn some powerful mathematics. But it remains necessary to re-enforce the most basic practical type