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Circle Area and Circumference Calculation

Calculate the area and circumference of circles using the π button on the calculator. Provide answers correct to one decimal place.

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Circle Area and Circumference Calculation

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  1. 1. Find the area and circumference of each of the following circles.Use theπbutton on the calculator and give your answer correct to one decimal place. (i) Area = πr2 = π(6)2 = 36π = 113·1 cm2 Circumference = 2πr = (2)(π)(6) = 12π = 37·7 cm

  2. 1. Find the area and circumference of each of the following circles.Use theπbutton on the calculator and give your answer correct to one decimal place. (ii) Area = πr2 = π(9)2 = 81π = 254·5 cm2 Circumference = 2πr = (2)(π)(9) = 18π = 56·5 cm

  3. 1. Find the area and circumference of each of the following circles.Use theπbutton on the calculator and give your answer correct to one decimal place. (iii) Area = πr2 = π(8)2 = 64π = 201·1 cm2 Circumference = 2πr = (2)(π)(8) = 16π = 50·3 cm

  4. 2. Given the area of a circle is 6∙25π m2, find the length of its radius and hence the circumference of the circle, in terms of π. Area = 6·25π Area = πr2 Circumference = 2πr = 2π (2·5) = 5π m

  5. 3. Given the area of a circle is 154 cm2, find the length of its radius and hence the circumference of the circle. Take πas . Area of circle = πr2 = 154

  6. 4. Given the circumference of a circle is 30πm, find the length of its radius and hence the area of the circle, in terms of π. Circumference of circle = 2πr 2πr = 30π 2r = 30 r = 15 m Area of circle = πr2 = π(15)2 = 225π m2

  7. 5. Given the circumference of a circle is 157 cm, find the length of its radius and hence the area of the circle. Take πas 3∙14. Circumference of circle = 2πr Area of circle = πr2 = (3·14)(25)2 = (3·14)(625) = 1962·5 cm2

  8. 6. A sector of angle 30° is removed from a circle of radius 5 cm, as shown. (i) What fraction of the circle has been removed?

  9. 6. A sector of angle 30° is removed from a circle of radius 5 cm, as shown. (ii) Find the area of the circle remaining. Give your answer to one decimal place.

  10. 7. For each of the following sectors, find the (a) area and (b) length of the arc. Give your answers in terms of π. (i) Radius =

  11. 7. For each of the following sectors, find the (a) area and (b) length of the arc. Give your answers in terms of π. (i)

  12. 7. For each of the following sectors, find the (a) area and (b) length of the arc. Give your answers in terms of π. (ii)

  13. 7. For each of the following sectors, find the (a) area and (b) length of the arc. Give your answers in terms of π. (ii)

  14. 7. For each of the following sectors, find the (a) area and (b) length of the arc. Give your answers in terms of π. (iii) Angle = 60˚

  15. 7. For each of the following sectors, find the (a) area and (b) length of the arc. Give your answers in terms of π. (iii)

  16. 7. For each of the following sectors, find the (a) area and (b) length of the arc. Give your answers in terms of π. (iv) Angle = 270˚

  17. 7. For each of the following sectors, find the (a) area and (b) length of the arc. Give your answers in terms of π. (iv)

  18. 7. For each of the following sectors, find the (a) area and (b) length of the arc. Give your answers in terms of π. (v) Angle = 120˚

  19. 7. For each of the following sectors, find the (a) area and (b) length of the arc. Give your answers in terms of π. (v)

  20. 7. For each of the following sectors, find the (a) area and (b) length of the arc. Give your answers in terms of π. (vi) Angle = 315˚

  21. 7. For each of the following sectors, find the (a) area and (b) length of the arc. Give your answers in terms of π. (vi)

  22. 8. Find the perimeter of each of the following sectors. Use the πbutton on the calculator and give your answer correct to one decimal place. (i) Angle = 72˚

  23. 8. Find the perimeter of each of the following sectors. Use the πbutton on the calculator and give your answer correct to one decimal place. (i)

  24. 8. Find the perimeter of each of the following sectors. Use the πbutton on the calculator and give your answer correct to one decimal place. (ii) Angle = 225˚

  25. 8. Find the perimeter of each of the following sectors. Use the πbutton on the calculator and give your answer correct to one decimal place. (ii)

  26. 9. Find the area of the shaded region for each of the following. Give your answer correct to one decimal place. (i) Area of shaded region = Area of square − Area of circle = L2 – πr2 = (8)2 – π(4)2 = 64 − 16π = 13·73 = 13·7 cm2

  27. 9. Find the area of the shaded region for each of the following. Give your answer correct to one decimal place. (ii)

  28. 10. A game at a fun fair consists of spinning a spinner, which has five equal sectors. If the radius of the spinner is 35 cm, find the area of one of the sectors of the spinner. Give your answer correct to one decimal place.

  29. 11. A sports club is having a target painted on a wall so that its members can practice taking shots. If the target is to be painted as shown, what area of the wall will be painted with pink paint? Give your answer correct to one decimal place. Area covered in pink = Inner circle + Outer ring (Big circle − Smaller circle)

  30. 12. Find the area of the following compound shapes. Give your answer correct to two decimal places. (i) Area of shape = Area of rectangle + Area of circle

  31. 12. Find the area of the following compound shapes. Give your answer correct to two decimal places. (ii) Area of shape = Area of rectangle + Area of circle

  32. 12. Find the area of the following compound shapes. Give your answer correct to two decimal places. (iii) Area of shape = Area of triangle + Area of semi-circle

  33. 13. A garden has a shape as shown. (i) Find the area of the garden, giving your answer correct to two decimal places. Area of garden = Area of rect. A + Area of triangle B + Area of rect. C + Area of circle D

  34. 13. A garden has a shape as shown. (ii) The garden is to be covered with artificial grass. The cost of the grass is €35 per square metre, plus €7∙50 per square metre for fitting. VAT of 18% is then applied. Find the total cost of buying and fitting the grass. Give your answer to the nearest euro. Cost per m2 = €35 + €7·50 = €42·50 Cost ex. VAT = (€42·50 × 70·283) = €2987·03 Cost inc. 18% VAT = €2987·03 × 1·18 = €3524·70

  35. 14. Circular lids are cut out of a rectangular sheet of tin. The factory wants to waste as little tin as possible, so the three identical circles fit perfectly inside the rectangle, as shown. Given the width of the rectangle is 22 cm, find the area of the tin remaining, after the lids have been cut out. Take π = 3∙14 and give your answer correct to one decimal place. Radius of one circle = 11 cm Length of the rectangle = 3 × 22 = 66 cm Area of tin remaining = Area of rectangle − Area of 3 circles = (L × W) – 3(πr2) = (66)(22) − 3π(11)2 = 1452 − 1139·82 = 312·18 = 312·2 cm2

  36. 15. A sector of a circle, centrePand radius |PQ| = 8 cm is drawn inside a square PQRS. (i) Find the area of the triangle PQS.

  37. 15. A sector of a circle, centrePand radius |PQ| = 8 cm is drawn inside a square PQRS. (ii) Find the area of the sector, correct to one decimal place.

  38. 15. A sector of a circle, centrePand radius |PQ| = 8 cm is drawn inside a square PQRS. (iii) Hence find the area of the segment from Q to S (shaded area). Area of segment = Area of sector − Area of triangle = 50·3 − 32 = 18·3 cm2

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