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Mathematics 7th grade با پاسخ UNIT 18: Area‚ perimeter and volume 18.5 Calculating the surface area of cubes and cuboids

آخرین ویرایش: 11:04   1401/06/30 36 گزارش خطا

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.

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.

c
b
a

2) Work out the surface area of each of these cuboids.

b
a

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