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KS3 Mathematics

KS3 Mathematics. S8 Perimeter, area and volume. S8 Perimeter, area and volume. Contents. S8.2 Area. S8.3 Surface area. S8.1 Perimeter. S8.4 Volume. S8.5 Circumference of a circle. S8.6 Area of a circle. Perimeter. 1 cm.

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KS3 Mathematics

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  1. KS3 Mathematics S8 Perimeter, area and volume

  2. S8 Perimeter, area and volume Contents S8.2 Area S8.3 Surface area S8.1 Perimeter S8.4 Volume S8.5 Circumference of a circle S8.6 Area of a circle

  3. Perimeter 1 cm To find the perimeterof a shape we add together the length of all the sides. What is the perimeter of this shape? Starting point Perimeter = 3 + 3 + 2 + 1 + 1 + 2 3 = 12 cm 2 3 1 1 2

  4. Perimeter Sometime we are not given the lengths of all the sides. We have to work them out from the information we are given. 9 cm a = 12 – 5 = 7 cm 5 cm 9 – 4 b = 12 cm 4 cm = 5 cm a cm 7 cm P = 9 + 5 + 4 + 7 + 5 + 12 = 42 cm b cm 5 cm

  5. S8 Perimeter, area and volume Contents S8.1 Perimeter S8.3 Surface area S8.2 Area S8.4 Volume S8.5 Circumference of a circle S8.6 Area of a circle

  6. Area Rug A Rug C Rug B The area of a shape is a measure of how much surface the shape takes up. For example, which of these rugs covers a larger surface?

  7. Area of a rectangle length, l Area of a rectangle = length × width width, w = lw Area is measured in square units. For example, we can use mm2, cm2, m2 or km2. The 2 tells us that there are two dimensions, length and width. We can find the area of a rectangle by multiplying the length and the width of the rectangle together.

  8. Area of a rectangle What is the area of this rectangle? 4 cm 8 cm Area of a rectangle = lw = 8 cm × 4 cm = 32 cm2

  9. Area of shapes made from rectangles How can we find the area of this shape? We can think of this shape as being made up of two rectangles. 7 m Either like this … A 10 m … or like this. 15 m 8 m Label the rectangles A and B. B 5 m Area A = 10 × 7 = 70 m2 15 m Area B = 5 × 15 = 75 m2 Total area = 70 + 75 = 145 m2

  10. S8 Perimeter, area and volume Contents S8.1 Perimeter S8.2 Area S8.3 Surface area S8.4 Volume S8.5 Circumference of a circle S8.6 Area of a circle

  11. Making cuboids The following cuboid is made out of interlocking cubes. How many cubes does it contain?

  12. Making cuboids We can work this out by dividing the cuboid into layers. The number of cubes in each layer can be found by multiplying the number of cubes along the length by the number of cubes along the width. 3 × 4 = 12 cubes in each layer There are three layers altogether so the total number of cubes in the cuboid = 3 × 12 = 36 cubes

  13. Making cuboids The amount of space that a three-dimensional object takes up is called its volume. Volume is measured in cubic units. For example, we can use mm3, cm3, m3 or km3. The 3 tells us that there are three dimensions, length, width and height. Liquid volume or capacity is measured in ml, l, pints or gallons.

  14. Volume of a cuboid Volume of a cuboid = length × width × height = lwh We can find the volume of a cuboid by multiplying the area of the base by the height. The area of the base = length × width So, height, h length, l width, w

  15. Volume of a cuboid What is the volume of this cuboid? Volume of cuboid = length × width × height 5 cm = 5 × 8 × 13 13 cm 8 cm = 520 cm3

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