Embed Size (px)
Citation preview
1
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 rectanglesolve problems involving surface areas and volumes of prisms, pyramids, cylinders, cones and spheressolve problems involving more complex shapes and solids, including segments of circles and frustums of conescalculate perimeters and areas of shapes made from triangles and rectanglesfind the surface area of simple shapes using the formulae for the areas of triangles and rectanglesareas of parallelograms and trapeziums, halfcircles 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 cuboidsconvert between area measures, including square centimetres and square metres, and volume measures, including cubic centimetres and cubic metresfind circumferences of circles and areas enclosed by circles, recalling relevant formulaecalculate the lengths of arcs and the areas of sectors of circles
2
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)
3
Sketch in your book:
A rectangle with area 36cm2.
A square with area 36cm2.
A parallelogram with area 36cm2.
A triangle with area 36cm2.
A trapezium with area 36cm2.
A circle with area 36cm2.
4
Area of a triangle without the height.
A
BCProve 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?
page 472 E4and E5
5809cm
16cm
5
6
7
Circles
Area of a circle =
Area of a sector of the circle=
0
1300
page 244 A1: a,c,eA2A8 even nos only
Area of a Segment
120
page 246
10cm
8
Surface Area
page 97 a and c
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
9
Volume
volume
page 96 E1, E4 and E6
10
Functional skills task page 48
11
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
12
Volume and surface Area of Cylinders
Page 247 C3 and odds only
10cm
15cm
13
Converting Units
convert 1m to cm2 2
page 100
14
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
15
Homework:Make a cone with volume approximately 150cm3.Stick it onto a piece of paper showing your working.Find its surface area.
16
Surface area of a cone
h
r
Surface area =
Find the surface area of the cone.
Page 252 D15 odds only
D 13, D14
17
FrustrumT
A frustrum is a cone with the top taken off.
18
Volume and Surface Area of a sphere
SA (sphere) =
Volume of a sphere =
Page 255 Odds only
19
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
20
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.
21
22
Exam questionA 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.
23
Density
Which weighs more a kg of flour of a kg of feathers?
page 99 odds only
24
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?
