use their knowledge of rectangles, parallelograms and triangles to deduce formulae for the area of a parallelogram, and a triangle, from the formula for the area of a rectangle solve problems involving surface areas and volumes of prisms, pyramids, cylinders, cones and spheres solve problems involving more complex shapes and solids, including segments of circles and frustums of cones calculate perimeters and areas of shapes made from triangles and rectangles find the surface area of simple shapes using the formulae for the areas of triangles and rectangles areas of parallelograms and trapeziums, half circles and quarter circles find volumes of cuboids, recalling the formula and understanding the connection to counting cubes and how it extends this approach calculate volumes of right prisms and of shapes made from cubes and cuboids convert between area measures, including square centimetres and square metres, and volume measures, including cubic centimetres and cubic metres find circumferences of circles and areas enclosed by circles, recalling relevant formulae calculate the lengths of arcs and the areas of sectors of circles 1
Area and Volume area Prove that the area of a parallelogram is base x height h Pages 91 93 do a,c,e only (for questions that have parts) 2
Sketch in your book: A rectangle with area 36cm 2. A square with area 36cm 2. A parallelogram with area 36cm 2. A triangle with area 36cm 2. A trapezium with area 36cm 2. A circle with area 36cm 2. 3
Area of a triangle without the height. A C B Prove that the area of this triangle is 1/2 ab sinc. Hint: draw in the height. In order to use this formula, what info do you need? 16cm 58 0 9cm page 472 E4and E5 4
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Circles Area of a circle = Area of a sector of the circle= 130 0 0 page 244 A1: a,c,e A2 A8 even nos only Area of a Segment 10cm 120 page 246 7
Surface Area The surface area of a shape is the total area of all surfaces. Find the surface area of 1) a 10cm cube 2) a cuboid 2x3x4cm page 97 a and c 8
Volume volume page 96 E1, E4 and E6 9
Functional skills task page 48 10
Homework for next Monday 1) Area of segments: page 246 B1 B2 optional ext B5 a) 2) Surface area: page 98 E8 3) Volume: page 96 E3, E5 4) Vol and SA of cylinder: page 247 C4, C10 11
Volume and surface Area of Cylinders 10cm 15cm Page 247 C3 and odds only 12
Converting Units 2 2 convert 1m to cm page 100 13
Volume of a pyramid and a cone You will need thin card, scissors and glue page 249: draw the net accurately and put it together. Working in groups of 4, each person needs to make an an accurate copy of the net (page 249) Using your pyramids, copy and complete the table. Volume of a pyramid 14
Homework: Make a cone with volume approximately 150cm 3. Stick it onto a piece of paper showing your working. Find its surface area. 15
Surface area of a cone Surface area = h r Find the surface area of the cone. Page 252 D15 odds only D 13, D14 16
T Frustrum A frustrum is a cone with the top taken off. 17
Volume and Surface Area of a sphere SA (sphere) = Volume of a sphere = Page 255 Odds only 18
Homework 1. Make a bookmark/poster/notecard with formulae on, in order to help you learn them. You must include all of the following: Area of a triangle a circle parallelogram trapezium Surface area of a cone a sphere Volume of: a cylinder a pyramid a cone a sphere For Thursday 01/03/07 19
This cone has diameter 18cm and height 20cm. Find its volume. There are 1+ 3 + 5 + 8 + 11 chocolate balls in the cone each with radius 1cm. Find the percentage of chocolate in the cone. If you were to make a solid chocolate ball with the same volume as the sphere what would its radius be? A cone and a sphere have radius 10cm and the same volume. What is the height of the cone? A cone and a sphere have radius 8cm and the same volume. What is the height of the cone? What do you notice about both answers? Prove that h=4r if both the sphere and the cone have the same radius and volume. 20
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Exam question A sphere of radius 3cm has the same volume as a cylinder with radius 2 cm. Find the height of the cylinder. A sphere of radius r cm has the same volume as a cylinder with radius 2 cm and height h. Express r in terms of h. 22
Density Which weighs more a kg of flour of a kg of feathers? page 99 odds only 23
Population Density Population Density means how many people are there per square metre? How dense is the population? ie how tightly packed..not how stupid?.. What is the approximate popn density of this classroom? 24