Mathematics 7th grade با پاسخ UNIT 18: Area‚ perimeter and volume 18.5 Calculating the surface area of cubes and cuboids
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Mathematics 7
- UNIT 1: Integers
- 1.1 Using negative numbers
- 1.2 Adding and subtracting negative numbers
- 1.3 Multiples
- 1.4 Factors and tests for divisibility
- 1.5 Prime numbers
- 1.6 Squares and square roots
- End of unit review
- UNIT 2: Sequences‚ expressions and formulae
- 2.1 Generating sequences (1)
- 2.2 Generating sequences (2)
- 2.3 Representing simple functions
- 2.4 Constructing expressions
- 2.5 Deriving and using formulae
- End of unit review
- UNIT 3: Place value‚ ordering and rounding
- 3.1 Understanding decimals
- 3.2 Multiplying and dividing by 10‚ 100 and 1000
- 3.3 Ordering decimals
- 3.4 Rounding
- 3.5 Adding and subtracting decimals
- 3.6 Multiplying decimals
- 3.7 Dividing decimals
- 3.8 Estimating and approximating
- End of unit review
- UNIT 4: Length‚ mass and capacity
- 4.1 Knowing metric unit
- 4.2 Choosing suitable units
- 4.3 Reading scales
- End of unit review
- UNIT 5: Angles
- 5.1 Labelling and estimating angles
- 5.2 Drawing and measuring angles
- 5.3 Calculating angles
- 5.4 Solving angle problems
- End of unit review
- UNIT 6: Planning and collecting data
- 6.1 Planning to collect data
- 6.2 Collecting data
- 6.3 Using frequency tables
- End of unit review
- UNIT 7: Fractions
- 7.1 Simplifying fractions
- 7.2 Recognising equivalent fractions‚ decimals and percentages
- 7.3 Comparing fractions
- 7.4 Improper fractions and mixed numbers
- 7.5 Adding and subtracting fractions
- 7.6 Finding fractions of a quantity
- 7.7 Finding remainders
- End of unit review
- UNIT 8: Symmetry
- 8.1 Recognising and describing 2D shapes and solids
- 8.2 Recognising line symmetry
- 8.3 Recognising rotational symmetry
- 8.4 Symmetry properties of triangles‚ special quadrilaterals and polygons
- End of unit review
- UNIT 9: Expressions and equations
- 9.1 Collecting like terms
- 9.2 Expanding brackets
- 9.3 Constructing and solving equation
- End of unit review
- UNIT 10: Averages
- 10.1 Average and range
- 10.2 The mean
- 10.3 Comparing distributions
- End of unit review
- UNIT 11: Percentages
- 11.1 Simple percentages
- 11.2 Calculating percentages
- 11.3 Comparing quantities
- End of unit review
- UNIT 12: Constructions
- 12.1 Measuring and drawing lines
- 12.2 Drawing perpendicular and parallel lines
- 12.3 Constructing triangles
- 12.4 Constructing squares‚ rectangles and polygons
- End of unit review
- UNIT 13: Graphs
- 13.1 Plotting coordinates
- 13.2 Lines parallel to the axes
- 13.3 Other straight lines
- End of unit review
- UNIT 14: Ratio and proportion
- 14.1 Simplifying ratios
- 14.2 Sharing in a ratios
- 14.3 Using direct proportion
- End of unit review
- UNIT 15: Time
- 15.1 The 12-hours and 24-hours clock
- 15.2 Timetables
- 15.3 Real-life graphs
- End of unit review
- UNIT 16: Probability
- 16.1 The probability scale
- 16.2 equally likely outcomes
- 16.3 Estimating probabilities
- End of unit review
- UNIT 17: Position and movement
- 17.1 Reflection shapes
- 17.2 Rotation shapes
- 17.3 Translating shapes
- End of unit review
- UNIT 18: Area‚ perimeter and volume
- 18.1 Converting between units for area
- 18.2 Calculating the area and perimeter of rectangles
- 18.3 Calculating the area and perimeter of compound shapes
- 18.4 Calculating the volume of cuboids
- 18.5 Calculating the surface area of cubes and cuboids
- End of unit review
- UNIT 19: Interpreting and discussing the results
- 19.1 Interpreting and drawing pictograms‚ bar charts‚ bar-line graphs and frequency diagram
- 19.2 Interpreting and drawing pie charts
- 19.3 Drawing conclusions
- End of unit review
- End of year review
The surface area of a cube or cuboid is the total area of all its faces.
The units of measurement for surface area are square units, for example, mm2,cm2 or m2.
This cube has six faces.
The area of one face =2×2
=4cm2
The surface area of the cube =6×4
=24cm2
This is a net of a cuboid. It can be folded up to make the cuboid shown.
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You can see that the cuboid has two blue faces, two red faces and two green faces.
Area of one red face = length × width
Area of one blue face = length × height
Area of one green face = width × height
To work out the surface area you need to add together the areas of all the faces. This cuboid has two faces of each colour so you would need to multiply the area of each face by 2, before adding them all together.
Worked example 18.5
Work out the surface area of this cuboid.
Area of top face =8×5=40cm2
Use the formula: area = length × width
Area of front face =8×3=24cm2
Use the formula: area = length × height
Area of side face =5×3=15cm2
Use the formula: area = width × height
Surface area =2×40+2×24+2×15
Multiply the area of each face by 2.
=80+48+30
Add the areas to find the total surface area.
=158cm2
Remember to include the units in your answer.
Exercise 18.5
1) Work out the surface area of each of these cuboids.
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2) Work out the surface area of each of these cuboids.
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3) a: Work out the surface area of this cuboid.
b: Show how to use estimation to check your answer to part a.
4) Work out the surface area of this cuboid.
Give your answer in:
а: mm
b: cm?
5) Michiko has a metal container in the shape of a cuboid.
The container is 2/4m long, 1/2m wide and 0/6m high.
Michiko plans to paint all the outside faces of the container with two coats of metal paint.
a: How many tins of paint does Michiko need to buy?
b: What is the total cost of the paint?
Size of tin: 250ml
Paint coverage: 4/52m
Summary
You should now know that:
* Area is measured in square units such as square metres (cm2), square centimetres (cm2) and square millimetres (mm2).
* The conversion factors for area are:
1cm2=100mm2,1m2=10000cm2
* The formula for the area of a rectangle is:
area = length × width.
* The perimeter of a shape is found by adding the lengths of all the sides together.
* To find the area of a compound shape:
1) split the shape up into squares and/or rectangles
2) work out the area of each individual square or rectangle
3) add together the individual areas to get the total area.
* The formula for the volume of a cuboid is:
volume = length × width × height.
* The surface area of a cube or cuboid is the total area of all its faces.
You should be able to:
* Convert between units for area, for example, m2,cm2 and mm2.
* Derive and use formulae for the area and perimeter of a rectangle.
* Calculate the perimeter and area of compound shapes made from rectangles.
* Derive and use the formula for the volume of a cuboid.
* Calculate the surface area of cubes and cuboids from their nets.
* Understand everyday systems of measurement and use them to estimate and calculate.
* Work logically and draw simple conclusions.