Revision of Grade 12 Space and Shape Part 2 3D Shapes

Transcription

1 Saturday X-tra X-Sheet: 13 Revision of Grade 12 Space and Shape Part 2 3D Shapes Key Concepts In this session we will focus on summarising what you need to know about: - Measurements of capacity and volume - Volume of prisms Terminology & definitions - Capacity is the volume of a 3D container or shape - Volume is a measure of the amount that can be held or contained by something (container). - Capacity or volume is measured in units CUBED, e.g. cm 3 or m 3. The capacity of fluids can be measured in millilitres, litres or kilolitres. Conversions to know: - 1cm 3 = 1000mm 3-1cm 3 = 1ml 1cm 10mm 1cm 3 1cm = 1000mm 3 10mm 1cm 10mm cm 3 = 1000ml = 1 litre - 1m 3 = cm 3 = 1000 litres = 1 kilolitre - 1km 3 = m 3 - Volume of a prism = area of cross section x length of prism Page 1

2 Common volumes of prisms: - Volume of a rectangular prism = length x breadth x height length height breadt - Volume of a cylinder = area circle x height = = h = Height / length - Volume of triangular prism = area of triangle x length - = ½ base x height of triangle x length Area triangle = ½ base x height length Concept: Measurement of Capacity and Volume X-ample 1: 0.11 cm 3 = mm 3 X-ample 2: 150 ml = cm 3 Page 2

3 X-ample 3: 352 m 3 = l = kl X-ample 4: 123 kl = m 3 Concept: Volumes of prisms X-ample 5: Thomas buys a small fish tank from "Fish World" for R199,99. The dimensions of the fish tank are 91 cm by 32 cm by 35 cm. 35 cm 32 cm 1. a. Calculate the volume of the tank in cm 3. b. Convert the volume of the tank into m How many litres of water will the tank hold when full? X-ample 6: 91 cm 1000 cm 3 = 1 litre Lebo purchased a cylindrical water container to store her treated drinking water. The height of the container is 60 cm and the radius is 20 cm, as shown below. Calculate the volume of the water container. Use the formula: Volume of cylinder = π x (radius) 2 x height using π= 3,14. Page 3

4 X-ample 7: This is a diagram of the cross section of a swimming pool. 1 Calculate the volume of the whole pool. 2 If the pool is only 95% filled how much water is needed? 1m 3 = 1kl 3 If the pool is filled at a rate of 500 litres per hour how long will it take to fill the tank? Area of a trapezium = ½ (length of top + length of bottom) x height of trapezium Volume of a prism = area of cross section x length X-ample 8: Each small equilateral triangular Toblerone box has the following dimensions: 5 cm 20cm Find the volume of the box. Give your answer to 1 decimal place. Page 4

5 X-ample 9: Ronwyn and Bronwyn are twins. They plan to celebrate their 21st birthday by having a big party. Ronwyn has decided that she wants a round cake, while Bronwyn has decided to have a ring cake, as shown in the pictures below. The dimensions of each cylindrical cake are as follows: The following formulae (using π = 3,14) may be used: Volume of a cylinder = π (radius) 2 height Volume of a cylindrical ring = π (R 2 r 2 ) height where R = outer radius and r = inner radius Using the volume of each cake, determine which of the two cakes is better value for money if the costs of the two cakes are the same. Give a reason for your answer, showing ALL your calculations. Page 5

6 X-ample 10: Ben wants to work out the volume of a can of beans. According to his measurements, the can measures 74mm from one side of the top to the other (diameter). The can is also 109 mm high. Find the volume of the tin. = X-ample 11: Find the volume of the rectangular prism, in kilolitres. Volume of a rectangular prism = length x breadth x height 10m 5m 2m X-ercise 1. Find the volume of the triangular prism. Give your answer to 1 d.p. 6 cm 10cm Page 6

7 2. A circular pool above the ground has a diameter of 7,5 m and a height of 2 m. Calculate the volume (in m 3 ) of the pool. Give your answer rounded off to one decimal place. 3. Cailin's LCD TV screen is a new slim model that is only 39,7 mm thick. The rectangular screen is 45 cm high and 60 cm wide. The TV stands on a round base with a diameter of 20 cm that is 2 cm thick and is held up by a swivel that is 5 cm high, as shown in the diagram below. Determine the volume (in cm 3 ) of the rectangular box that the TV will be delivered in if there is an allowance of 2 cm (on both sides) for all measurements to package the TV, as shown in the side view above. Given the formula: Volume = length x breadth x height Page 7

8 X-ercise Answers. 1. height = 5, cm Volume = area triangle x length = ½(6 x 5,196 ) x 10 = 155,9cm 3 2. Volume = ח r 2 h = ח) 3,14 ; r = 3,75m ; h = 2) Volume = 3,14 x (3,75) 2 x 2 = 88, ,3 m 3 (1 d.p) 3. Total height of the TV = = 52cm Total breadth of the TV = 20 cm Total length of the TV = 60cm Add 2cm on either side of the height, breadth and length (+ 4 cm) Dimensions of the box: Height = = 56cm Breadth = = 24cm Length = = 64cm Volume of the BOX = 56 x 24 x 64 = cm 3 Page 8