ࡱ> fhe#` bjbjmm >000D----$-dDtU, . . . . .PPPTTTTTTT$VhYU0PqHtPPPU . .Q.UTTTP8 .0 .TTPTTT0T .. _Y-QTTDU0tUTYRYTTY0T$PPTPPPPPUUTPPPtUPPPPDDD&,DDD,DDD  Areas and Volumes. 1. Area Area is the amount of space that is enclosed within a 2-D shape. There are many units of area, some common metric ones are : mm2, cm2, km2 You may have used other imperial units such as square inches, square feet, square yards and square miles. Well concentrate on the metric units in this worksheet.  Area of a rectangle : This is calculated by multiplying the width of the shape by the length. Example : Calculate the area of the shape shown : 13cm  5cm not to scale Area = 13 x 5 = 65cm2  Area of a triangle This is calculated by multiplying half of the length of the base by the height.  Example : Calculate the area of the shape shown :  Area = x 6 x 7 = 3 x 7 7cm = 21cm2   6cm not to scale When calculating the area of a triangle, make sure you use the height and not the length of one of the sides :  height 5cm 4cm  not to scale Some difficult shapes Some questions will not just involve one shape but maybe 2 or 3, like this : Example : Calculate the area of the shape shown :   6cm 3cm  7cm  not to scale  14cm We first have to split the large L shaped figure into two separate rectangles and work out the sides that we need to calculate the area like this :   6cm 3cm  7cm  14 ( 6 = 8cm 7 ( 3 = 4cm  not to scale  14cm Now we have two rectangles we can work out the area of each rectangle and add the two areas together to get the area of the L-shape like this :   Area = 6 x 7 = 42cm2 Area = 8 x 4 = 32cm2 Total area = 42 + 32 = 74cm2 Volume This is the amount of space enclosed within a 3-D object. Common units are cm3, m3 and km3. Note also that cm3 can also be described as litres. Example Find the volume of this cuboid :   5cm  12cm 10cm not to scale To find the volume of a cuboid we use :  Volume of a cuboid = height x width x length In this case : Volume = 5 x 10 x 12 = 600cm3 Exercise 7.1 1. Work out the area of this shape :  4cm 12cm not to scale 2. The plan view of a hotel room is shown below. Find the area of the floor. 4m  not to scale  4m 3m  7m 3. A triangular road sign has a base dimension of 60cm and a height of 60cm. Work out its area in (a) cm2 (b) m2 (hint convert 60cm to m first) 4. A small aircraft has passenger windows that are squares with sides of 40cm. (a) Work out the area of each window in cm2 (b) If there are 50 windows, find the total area of glass in square metres. (c) The front windscreen of the aircraft is a rectangle as shown below :  Calculate the area of 1.2m the windscreen in m2 not to scale 2m 5. Fabien wants to fill this cake tin with mixture. How does he calculate the correct volume of the cake mixture?  6cm  20cm  not to scale 20cm (a) 20 + 20 + 6 (b) 20 + 20 + 6 x 2 (c) 20 x 2 x 6 (d) 20 x 20 x 6 6. The units for measuring the volume of the cake mixture in Q5 are : (a) cm3 (b) cm2 (c) cm (d) m3 7. A swimming pool has a constant depth of 2m. It is 25m long and 10m wide. Calculate the volume of water required to completely fill it. 8. The waiting room at an airport is a cube with the dimensions of 9m. (a) What is the area of one of the walls? (b) What is the area of all 4 walls? (c) What is the total area of the four walls and the ceiling together? (d) If one tin of paint will cover 50m2, then how many tins are needed to paint the 4 walls and ceiling? (e) What is the volume of the room? 9. A notice board has to have an area of 9 square metres. The board measures 1.5m from top to bottom as shown. What is the length of the board? Length = ???  1.5m Area = 9m2 10. This is a drawing of a lawn and patio in a garden : 7m  PATIO   8m LAWN 6m not to scale  10m (i) Which of these is the correct way to find the area of the lawn? (a) (6 x 8) + (7 x 10) (b) (7 x 8) + (3 x 2) (c) (8 x 7) + (6 x 3) (d) (10 x 6) + (8 x 7) (ii) Calculate the area of the patio. Worksheet taken from : www.gcad-cymru.org.uk/vtc/ngfl/key_skills/20040825/018_area_and_volume.doc - _ ` a v T V X Y [ o p    : ŰŰŰŰŰŰsghECJOJQJ^J.jhECJOJQJU^JmHnHsH uhECJH*OJQJ^J.jhECJOJQJU^JmHnHsH uhECJOJQJ^J hEH*hEhE5CJOJQJ\^JhE5OJQJ\^JhE5>*OJQJ\^JhE5>*CJOJQJ\^J&\ ] ^ _ a w x        . / / V W Z [ o p   # : U V W ^ c w ' ( $a$ ^`: A S T W Y ^ _ ) * ? 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