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Re-turfing the lawn?

Practical problems!. Re-turfing the lawn?. The lawn is rectangular and measures 20 metres by 40 metres. Turf costs £8.50 per m 2 . How much will it cost to buy the turf?. Re-laying the drive?.

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Re-turfing the lawn?

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  1. Practical problems! Re-turfing the lawn? The lawn is rectangular and measures 20 metres by 40 metres. Turf costs £8.50 per m2. How much will it cost to buy the turf? Re-laying the drive? The drive is also rectangular and measures 8m by 16m. Each brick is 10cm by 20cm and costs £1.75. How many bricks are needed and what is the total cost?

  2. Re-Turfing the Lawn? The lawn is rectangular and measures 20 m by 40 m. Turf costs £8.50 per m2. How much will it cost to buy the turf ? How much turf is needed? Area of lawn = base x height of rectangle 20 40 = 800 m2 Cost of turfing the lawn = 800 x £ 8.50 = £6800.00

  3. Re-laying the Drive? 1 m2 = 1 m x 1 m = 100cm x 100cm = 10 000 cm2 The drive is also rectangular and measures 8 metres by 16 metres. Each brick is 20cm by 10cm and costs £1.75. How many bricks will be needed and how much will it cost? Area of each brick = 20 cm x 10 cm = 200cm2 Area of Drive = 8 m x 16 m = 128 m2 = 128 x 10 000 = 1 280 000 cm2

  4. Farmer Max The Problem: Farmer Max needs to create a new grazing area for his animals. He has 50m of fencing, which comes in 1m sections. How can he best construct the fencing to give the animals maximum room?

  5. Farmer Max He begins by looking at different rectangles… 15m 20m 5m 23m 10m 2m • Do these fields use 50m of fencing? • Which field gives the largest area for his sheep?

  6. FarmerMax Your turn! • Draw a table to show all the different rectangles that he could make. Remember he only has 50 pieces of fencing (and he uses all of them!). Try to put your results in a logical order. You may find some sketches help you to check your work. • Add another column to your table to show the area of each rectangle. Which one would be best for Farmer Max?

  7. 4cm B2 3cm 3cm 6cm A B C D 42cm2 16cm2 33cm2 48cm2 Hit key or click for ANSWER

  8. 4cm B2 3cm 3cm 24cm2 6cm 9cm2 3cm A A B C D 33cm2 42cm2 42cm2 16cm2 16cm2 48cm2 48cm2

  9. B3 3cm 4cm 2cm 2cm 3cm 2cm 9cm A B C D 35cm2 28cm2 16cm2 21cm2 Hit key or click for ANSWER

  10. B3 3cm 4cm 2cm 2cm 12cm2 12cm2 3cm 4cm2 2cm 9cm A B C D 28cm2 35cm2 16cm2 21cm2

  11. Area of a Compound Shape Next Slide 6cm 6 x 6 = 36cm2 0.5 x 6 x 6 = 18cm2 6cm 6cm Total = 36 + 18 = 54 cm2

  12. Area of a Compound Shape Next Slide 4cm Rectangle 7 x 10 = 70 cm2 10cm Triangle 0.5 x 7 x 4 = 14 cm2 7cm Total = 70 - 14 = 56 cm2

  13. B5 4cm 5cm 3cm 6cm A B C D 28cm2 35cm2 45cm2 42.5cm2 Hit key or click for ANSWER

  14. B5 4cm 10cm2 2cm 6cm 5cm 18cm2 3cm 6cm A B C D 28cm2 35cm2 45cm2 42.5cm2

  15. B8 4cm 1cm 1cm 6cm 3cm A B C D 15cm2 29cm2 20cm2 21cm2 Hit key or click for ANSWER

  16. B8 4cm 5cm2 1cm 6cm2 1cm 6cm 9cm2 3cm A B C D 20cm2 15cm2 15cm2 29cm2 29cm2 21cm2 21cm2

  17. A = r 2 Area of a Circle 5cm A = 3.14 x 5 x 5 = 78.50 cm2

  18. A = r 2 Area of a Sector of a Circle Whole Circle Next Slide A = 3.14 x 3 x 3 = 28.26 cm2 3cm Divide by 2 = 14.13 cm2

  19. A = r 2 Area of a Sector of a Circle Whole Circle Next Slide A = 3.14 x 4 x 4 = 50.24 cm2 8cm Divide by 2 = 25.12 cm2

  20. A = r 2 Area of a Sector of a Circle Whole Circle Next Slide A = 3.14 x 8 x 8 = 200.96 cm2 8cm Divide by 4 = 50.24 cm2

  21. Chequered cuboid problem This cuboid is made from alternate purple and green centimetre cubes. What is its surface area? Surface area = 2 × 3 × 4 + 2 × 3 × 5 + 2 × 4 × 5 = 24 + 30 + 40 = 94 cm2 How much of the surface area is green? 48 cm2

  22. Surface area of a cuboid To find the surfacearea of a shape, we calculate the total area of all of the faces. A cuboid has 6 faces. The top and the bottom of the cuboid have the same area.

  23. Surface area of a cuboid To find the surfacearea of a shape, we calculate the total area of all of the faces. A cuboid has 6 faces. The front and the back of the cuboid have the same area.

  24. Surface area of a cuboid To find the surfacearea of a shape, we calculate the total area of all of the faces. A cuboid has 6 faces. The left hand side and the right hand side of the cuboid have the same area.

  25. Surface area of a cuboid To find the surfacearea of a shape, we calculate the total area of all of the faces. Can you work out the surface area of this cubiod? 5 cm 8 cm The area of the top = 8 × 5 = 40 cm2 7 cm The area of the front = 7 × 5 = 35 cm2 The area of the side = 7 × 8 = 56 cm2

  26. Surface area of a cuboid To find the surfacearea of a shape, we calculate the total area of all of the faces. So the total surface area = 5 cm 8 cm 2 × 40 cm2 Top and bottom 7 cm + 2 × 35 cm2 Front and back + 2 × 56 cm2 Left and right side = 80 + 70 + 112 = 262 cm2

  27. Volume of a prism made from cuboids What is the volume of this L-shaped prism? 3 cm We can think of the shape as two cuboids joined together. 3 cm Volume of the green cuboid 4 cm = 6 × 3 × 3 = 54 cm3 6 cm Volume of the blue cuboid = 3 × 2 × 2 = 12 cm3 Total volume 5 cm = 54 + 12 = 66 cm3

  28. Volume of a prism Volume of a prism = area of cross-section × length Remember, a prism is a 3-D shape with the same cross-section throughout its length. 3 cm We can think of this prism as lots of L-shaped surfaces running along the length of the shape. If the cross-section has an area of 22 cm2 and the length is 3 cm, Volume of L-shaped prism = 22 × 3 = 66 cm3

  29. Volume of a prism What is the volume of this triangular prism? 7.2 cm 4 cm 5 cm Area of cross-section = ½ × 5 × 4 = 10 cm2 Volume of prism = 10 × 7.2 = 72 cm3

  30. Volume of a prism What is the volume of this prism? 12 m 4 m 7 m 3 m 5 m Area of cross-section = 7 × 12 – 4 × 3 = 84 – 12 = 72 cm2 Volume of prism = 5 × 72 = 360 m3

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