OUTCOME 2. Numeracy for practical purposes - measuring
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1 OUTCOME 2 Numeracy for practical purposes - measuring
2 Read and complete the following LESSON REVISION
3 MEASUREMENT REVISION 1. Use the conversion tables to change these measurements into the units shown (a) 3.2 km = m (b) 486 cm 2 = m 2 (c) km = m (d) 13 km 2 = m 2 (e) 197 mm = cm (f) cm 3 = km 3 (g) mm = m (h) 4 km 3 = mm 3 (i) km = m
4 MEASUREMENT REVISION CONTINUED 2. Fill in the missing values: (a) 1 kilogram = grams (b) 1 tonne = kg (c) 1 gram = milligrams (d) 1 hectare = m 2
5 MEASUREMENT REVISION CONTINUED 3. Find the perimeter of the following shapes:
6 MEASUREMENT REVISION CONTINUED 4. Find the circumference of the following:
7 MEASUREMENT REVISION CONTINUED 5. Using the conversion table, change any units as required, then calculate the perimeters of the shapes below:
8 MEASUREMENT REVISION CONTINUED 6. Find the area of each shape:
9 MEASUREMENT REVISION CONTINUED 6. Find the area of each shape continued:
10 MEASUREMENT REVISION CONTINUED 7. Find the area of each of the following shapes:
11 MEASUREMENT REVISION CONTINUED 7. Find the area of each of the following shapes continued:
12 MEASUREMENT REVISION CONTINUED 8. A swimming pool has a width of 5m and a length of 12 m. A 1m wide pathway is to be laid in concrete all around the pool. a. Make a sketch of the pool and path. b. Calculate the area of the path.
13 MEASUREMENT REVISION CONTINUED 9. Find the volume of the following shapes:
14 MEASUREMENT REVISION CONTINUED 9. Find the volume of the following shapes continued:
15 MEASUREMENT REVISION CONTINUED 10. A shipping container has the dimensions: 2.4m width, 6m depth and 3m height. (a) Draw the shipping container. (b) What is the volume inside the shipping container? ADVANCED (c) The container is to be painted. What is its surface area?
16 MEASUREMENT REVISION CONTINUED ADVANCED 11. Find the surface area of the following shapes:
17 MEASUREMENT REVISION CONTINUED ADVANCED 12. Find the surface area of the following shapes: Answers at end
18 Read and complete the following LESSON EXTENSION
19 MEASUREMENT EXTENSION You MUST show all relevant diagrams & working out. 1. Circling the Earth Imagine a wire which had been stretched tightly around the earth at the equator, is cut and its circumference increased by 20m. The wire is then replaced around the earth so that it is the same distance from the equator at every point. If the radius of the earth is 6335km: a. Could you now walk under the wire? b. Calculate the height in metres of the wire above the surface of the earth, to 1 decimal place.
20 MEASUREMENT EXTENSION CONTINUED 2. The Great Pyramid The construction of the Great Pyramid, one of the Egyptian pyramids, was commencing in 2550BC. It has a square base with sides of length 232.3m. Its original vertical height was 148.1m, but 10m has been lost from its top through damage and erosion over the years. It is estimated that it was built from 2.3 million limestone blocks, each with an average mass of 2.5 tonnes. Calculate: a. The original volume of the Great Pyramid, before it was damaged, to the nearest m 3. b. The volume of the surviving part of the pyramid. c. The average volume of each limestone block in m 3, to two decimal places. d. The approximate weight of the missing part of the Great Pyramid.
21 MEASUREMENT EXTENSION CONTINUED 3. Squares & Cubes A toy manufacturer wishes to design a wooden cube with square holes which extend all the way through the cube, in each of the cube s faces. The lengths of the sides of the square holes are one-third the length of each side of the cube and the total exterior surface area of the toy is 8m 2. Calculate: a. The length of the sides of the cube, to 4 decimal places. b. The volume of the wood in the toy.
22 MEASUREMENT EXTENSION CONTINUED 4. Spider trail In the room shown in the diagram there is a spider sitting at X, the mid-point of the edge of the ceiling. The spider can see a fly on the floor at Y, the mid-point of one edge of the floor. What is the length of the shortest path the spider must travel to reach the fly by walking along the wall, the ceiling or the floor?
23 MEASUREMENT EXTENSION CONTINUED 5. Farmer Green Farmer Green owns an irregularly shaped paddock, APQBRSTA, as shown in the diagram. Starting at A, he has measured distances in metres along AB as well as the distances at right angles from AB to each other corner of his paddock. Use this information to calculate: a. The total area of his paddock in hectares, correct to two decimal places. b. The length of fencing needed to enclose the paddock. Answers at end
24 SOLUTIONS
25 MEASUREMENT REVISION SOLUTIONS 1. a m b m 2 c m d m 2 e cm f km 2 g m h mm 3 i. 45k m 2. a g b kg c mg d m 2
26 MEASUREMENT REVISION SOLUTIONS 3. a. 31 mm b. 64 mm c. 68 m 4. a mm b mm c mm 5. a cm b cm c m 6. a. 75 cm 2 b. 42 m 2 c. 315 mm 2 d cm 2 7. a. 72 m 2 b. 252 mm 2 c mm 2 d m 2 e. 120 cm 2 f m 2 8. a. Sketch b. 38 m 2
27 MEASUREMENT REVISION SOLUTIONS 9. a cm 3 b cm 3 c cm 3 d cm a. Sketch b m 3 c m a. 384 cm b cm 2 c. 210 cm a cm 2 b cm 2
28 MEASUREMENT EXTENSION SOLUTIONS 1. Circling the Earth a. Yes b. 3.2 m 2. The Great Pyramid a m 3 b m 3 c m 3 d tonne 3. Squares & Cubes a m b m 3 4. Spider trail 5 m 5. Farmer Green a ha b m
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