Perimeter, Area, and Volume Exercises for Junior Certificate Ordinary Level

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Explore various mathematical problems involving perimeter, area, and volume for Junior Certificate Ordinary Level, including calculations for pizza bases, athletics tracks, rectangular cartons, orange juice glasses, swimming pool distances, and garden areas.

  • Math
  • Geometry
  • Junior Certificate
  • Area
  • Volume
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  1. Junior Certificate Ordinary Level Perimeter, Area and Volume www.mathsplus.ie www.mathsplus.ie www.mathsplus.ie

  2. (a) A small pizza has diameter 20 cm. A large pizza has diameter 30 cm. (i) What is the area of the base of a small pizza, to the nearest cm2. Area of circle = r2 = 102 = 314 159.. cm2 20 cm 10 cm 15 cm (ii) What is the area of the base of a large pizza, to the nearest cm2. Area of circle = 152 = 706 858.. 7 cm2

  3. (a) A small pizza has diameter 20 cm. A large pizza has diameter 30 cm. (iii) What is the difference in area between one large pizza and two small pizzas? = 707 cm2 Area of large pizza Area of 2 small pizzas = 314 2 628 cm2 79 cm2

  4. (b) An athletics track has a total length of 400 m. The track is made up of two parallel sides [ab] and [cd], and two semicircular ends as shown in the diagram. The diameters of the 1 2 22 7 __ 2 r a b l = ends, [ac] and [bd], measure 28 m each. ___ = 14 28 m 28 m = 44 m r = 14 c d 22 ___ (i) Taking as , calculate the length of one of the 7 one of the semicircular ends.

  5. (c) cm by A rectangular carton full of fruit juice measures 12 6 cm by 33 cm. (i) Find the volume of juice in the carton. Volume = length width height = 12 6 33 33 cm = 2376 cm3 6 cm 12 cm

  6. (c) cm by A rectangular carton full of orange juice measures 12 6 cm by 33 cm. (iii) of each The radius of each glass is 3 cm. Calculate the height Volume = 132 cm3 glass, correct to the nearest centimetre. Volume of cylinder = r2h ___ 3 cm = (3)2 9 h 132 33 cm h = 4 668 = 5 cm h 6 cm 12 cm

  7. (a) A swimming pool is 50 m in length. Mary swims 25 lengths of the pool. What distance, in kilometres, does Mary swim? 50 25= 1250 m = 1 25 km 1000 m = 1 km

  8. (b) surrounded A garden is made up of a rectangular lawn that is by a path. The garden is 16 m long and 10 m wide. The path is 2 m wide. 16 m 2 m 2 m 10 m 2 m 2 m (i) Find, in m2, the area of the garden. Area = 16 10 Length Breadth = 160 m2

  9. (b) surrounded A garden is made up of a rectangular lawn that is by a path. The garden is 16 m long and 10 m wide. The path is 2 m wide. 16 m 2 m 16 2 2 12 m 2 m 10 m 10 2 2 6 m 2 m 2 m (ii) Find, in m2, the area of the lawn. Length Breadth = 72 m2 Area = 12 6

  10. (b) surrounded A garden is made up of a rectangular lawn that is by a path. The garden is 16 m long and 10 m wide. The path is 2 m wide. 16 m 2 m 2 m 10 m 2 m 2 m (iii) Find, in m2, the area of the path. Area of garden = 160 m2 Area of lawn = 72 m2 Area of path = 88 m2

  11. (a) cm. A circle has a radius of 3 5 3 5 cm 22 7 Taking as , calculate the length of the circumference of the circle. Circumference = 2 r 22 7 = 2 3 5 = 22 cm

  12. (b) cm. A cube has side of length 2 (i) in cm3. Find the volume of this cube Volume = length length length = 2 2 2 2 cm = 8 cm3 (ii) cubes. A rectangular block is built using 18 of these Find the volume of the rectangular block in cm3. Volume of block = 18 8 = 144 cm3

  13. (b) A cube has side of length 2 cm. (iii) high. This rectangular block is 6 cm long, 6 cm wide and 4 cm Find its surface area in cm2. 4 cm 6 cm 6 cm Surface Area = 2(l b + l h + b h) = 2(6 6 + 6 4 + 6 4) = 2(36 + 24 + 24) = 2(84) = 168 cm2

  14. (c) diagram. A field has shape and measurements as shown in the 110 m 75 m 75 m 110 m 110 30 80 m 30 m 25 m 25 m 30 m (i) Find, in metres, the length of the perimeter of the field. 75 + 80 + 25 + 30+ 100 + 110 m Perimeter = = 460 m

  15. (c) diagram. A field has shape and measurements as shown in the 110 m 75 m 25 m 30 m (ii) Find, in m2, the area of the field. 110 75+ 30 25 = 8250 + 750 = 9000 m2 Area =

  16. (c) diagram. A field has shape and measurements as shown in the 110 m Area = 9000 m2 1 hectare = 10000 m2 75 m Area =9000 _____ 10000 = 0 9 hectares 25 m 30 m (iii) Mary bought the field at a cost of 20 000 per hectare. How much did Mary pay for the field? Cost = 0 9 20000 = 18 000

  17. (a) A rectangular box has measurements as shown. Find the volume of the box in cm3. 20 cm 5 cm 50 cm Volume = length width height = 50 20 5 = 5000 cm3

  18. (b) 56 cm. The front wheel of a bicycle has a diameter of (i) Calculate, in cm, the length of the radius of the wheel. 1 2 Radius = diameter 56 = 28 cm (ii) wheel. Calculate, in cm, the length of the circumference of the 22 7 . Take as . Circumference = 2 r 22 7 = 2 28 56 cm 28 cm = 176 cm

  19. (b) 56 cm. (iii) The front wheel of a bicycle has a diameter of How far does the bicycle travel when the wheel makes 250 complete turns? Give your answer in metres. One complete turn = 176 cm 250 complete turns = 176 250 1 metre = 100 cm . cm m 44 000 100 = = 440 m

  20. (c) cm. A solid metal cylinder has radius 4 cm and height 14 (i) Find the volume of the cylinder in terms of . Volume of cylinder = r2h = 42 14 4 cm = 16 14 = 224 cm3 14 cm

  21. (c) cm. A solid metal cylinder has radius 4 cm and height 14 (ii) Find the curved surface area of the cylinder in terms of . Curved surface area of cylinder = 2 rh = 2 4 14 4 cm = 8 14 = 112 cm2 CSA 14 cm

  22. (c) cm. A solid metal cylinder has radius 4 cm and height 14 (iii) Find the total surface area of the cylinder in terms of . Total surface area of cylinder = 2 rh + 2 r2 TSA = 112 + 32 cm2 4 cm TSA = 144 cm2 = 112 cm2 CSA 14 cm Area of circles = 2 r2 = 2 42 = 2 16 Area of circles = 32 cm2

  23. (b) The gable-end of a house has measurements as shown in the diagram. Find, in m2,the area of the bottom rectangle section of the gable-end. (i) Area of rectangle = Length breadth 1 5 m = 7 8 = 56 m2 7 m 8 m

  24. (b) The gable-end of a house has measurements as shown in the diagram. Find, in m2,the area of the top triangular section of the gable-end. 5 (ii) 1 2 1 2 Area of triangle = base height 1 5 m = 8 1 5 = 6 m2 7 m 8 m

  25. (b) The gable-end of a house has measurements as shown in the diagram. The cost of 5 litres of paint is 23. 5 litres of this paint will cover an area of 31 m2. Find the cost of painting the gable-end with this paint. (iii) 23 6 m2 1 5 m 5 litres = 31 m2 62 m2 23 7 m 56 m2 5 litres = 31 m2 Cost of paint = 2 23 8 m = 46

  26. (a) The length of each side of a square tile is 9 cm. What area, in cm2, will 12 of these tiles cover? Area of square = length2 = 92 = 81 cm2 9 cm Area of 12 squares = 81 12 = 972 cm2

  27. (b) (i) A circular disc has a radius of 5 cm. Taking as 3 14, find, in cm2, the area of the disc. Area of circle = r2 5 cm = 3 14 52 = 78 5 cm2

  28. (b) (ii) A rectangular piece of cardboard has measurements as shown. Two circular pieces, each of radius length 5 cm, are cut out of this rectangular piece of cardboard as shown. Find, in cm2, the area of the remaining piece of cardboard. 24 cm Area of rectangle = length breadth Remaining area 5 cm = 24 12 = 288 cm2 157 cm2 131 cm2 288 cm2 12 cm From part (i) Area of one disc = 78 5 cm2 Area of two discs = 78 5 2 cm2 and as usual, you are not paying attention! I can see you, It s 11:52 AM , Sunday, January 24, 2021 = 157 cm2

  29. (c) 15 cm. A solid metal cylinder has radius 10 cm and height (i) metal Taking as 3 14, find, in cm3, the volume of the 10 cm cylinder. Volume of cylinder = r2h 15 cm = 3 14 102 15 = 4710 cm3

  30. (c) 15 cm. A solid metal cylinder has radius 10 cm and height (ii) was The cylinder was melted down and half of the metal length 15 cm and width 14 cm. Calculate, in cm, its height, correct to one decimal place. 10 cm recast as a rectangular solid. This rectangular solid has Volume = length width height Volume = volume of cylinder 2 height 15 cm 1 2355 = 15 14 height 14 cm 15 cm 2355 = 210 height Volume of cylinder = 4710 cm3 from part (i) 1 2 height = 11 214 = 11 2 cm 4710 = 2355 cm3

  31. (c) A garden with a semicircular lawn and two flowerbeds has measurements as shown in the diagram. Taking as 3 14, find the area of the lawn, in m2. (ii) 6 m radius = 6 cm 12 m 1 2 _ 56 52 m2 Area of semicircle = r2 Area of lawn = 113 04 3 14 62 Area of circle = r2 113 04

  32. (c) A garden with a semicircular lawn and two flowerbeds has measurements as shown in the diagram. Find the area of the flowerbeds, in m2. (iii) 6 m 12 m Area of garden = 72 m2 _____ 15 48 m2 Area of lawn = 56 52 m2 Area of flowerbeds =

  33. (c) A garden with a semicircular lawn and two flowerbeds has measurements as shown in the diagram. Taking as 3 14, find the total perimeter of the semicircular lawn, in m. (iv) 6 m 12 m 1 2 _ Perimeter of semicircle = 2 r = 3 14 6 = 18 84 Total perimeter = 12+ 30 84 m

  34. (b) A solid rectangular block of wood has length 16 cm, width 4 cm and height 6 cm. (i) Find, in cm3, the volume of the block of wood. 6 cm 16 cm 4 cm Volume = length width height = 16 4 6 = 384 cm3

  35. (b) A solid rectangular block of wood has length 16 cm, width 4 cm and height 6 cm. (ii) Cubes with sides of length 2 cm, as shown, are made from the block of wood. Find the number of cubes that can be made from the block of wood. 2 cm Volume of cube = length length length = 2 2 2 Number of blocks = 6 8 = 48 2 2 = 8 cm3 From part (i) volume of block = 384 cm3 6 384 8 ____ george01 = 48 Number of blocks = 4 16

  36. (b) A solid rectangular block of wood has length 16 cm, width 4 cm and height 6 cm. (iii) Calculate, in cm2, the surface area of the block of wood. 6 cm 16 cm 4 cm Surface Area = 2 l b + 2 l h + 2 b h = 2 16 6 = 192 + 48 + 128 = 368 cm2 + 2 6 4 + 2 16 4

  37. (c) An athletics track has two equal parallel sides [PQ] and [SR] and two equal semi-circular ends with diameters [PS] and [QR]. |PQ| = |SR| = 153 metres, and |PS| = |QR| = 30 metres. P Q 153 m C = 2 r = 2 3 14 15 r = 15 m 30 m One semicircular end = 3 14 15 = 47 1 metres R S (i) Taking as 3 14, calculate the length of one of the semi-circular ends, correct to the nearest metre. The length of the two semicircular ends is the circumference of the circle

  38. (c) An athletics track has two equal parallel sides [PQ] and [SR] and two equal semi-circular ends with diameters [PS] and [QR]. |PQ| = |SR| = 153 metres, and |PS| = |QR| = 30 metres. P Q 153 m 153 m 47 m 47 m 30 m 153 m R S (ii) Calculate the total length of one lap of the track, correct to the nearest metre. The length of one lap = 153 + 47 + 153 + 47 = 400 metres

  39. (c) An athletics track has two equal parallel sides [PQ] and [SR] and two equal semi-circular ends with diameters [PS] and [QR]. |PQ| = |SR| = 153 metres, and |PS| = |QR| = 30 metres. P Q 153 m One lap = 400 m 5000 m =5000 400 47 m 47 m 1 minute = 60 seconds ____ = 12 5 laps 153 m R S (iii) Noir n ran a 5000 metre race on the above track in 15 minutes. Calculate, in seconds, the average time it took Noir n to complete one lap of the track during that race. Time for one lap = 15 60 12 5 ______= 72 seconds

  40. (a) A disc has a radius of 2 5 cm. Taking as 3 14, calculate, in cm2, the area of the disc. Area of circle = r2 2 5 cm 2 52 Area = 3 14 = 19 625 cm2

  41. (b) A rectangular garden has measurements as shown. (ii) (i) Find, in m2, the area of the garden. The garden is to be covered completely with square concrete slabs each of side 50 cm. Find the number of slabs required to cover the garden. Area of rectangle = length breadth = 18 9 = 162 m2 Area of slab = 0 5 0 5 100 cm = 1 m 18 m = 0 25 m2 Number of slabs =162 ____ 9 m 0 25 = 648 Area = 162 m2

  42. (c) cm by A rectangular carton full of orange juice measures 10 7 cm by 25 cm. (i) carton. Find, in cm3, the volume of orange juice in the Volume = length width height = 10 7 25 25 cm = 1750 cm3 7 cm 10 cm

  43. (c) cm by A rectangular carton full of orange juice measures 10 7 cm by 25 cm. (ii) The orange juice fills 14 cylindrical glasses exactly. Find, in cm3, the volume of each glass. Volume = length width height = 10 7 25 25 cm = 1750 cm3 Volume of each glass 1750 14 = 125 cm3 ____ = 7 cm 10 cm

  44. (c) cm by A rectangular carton full of orange juice measures 10 7 cm by 25 cm. (iii) calculate The radius of each glass is 2 4 cm. Taking as 3 14, Volume = 125 cm3 the height of each glass, correct to the nearest centimetre. Volume of cylinder = r2h _______ 2 4 cm = 3 14(2 4) 218 0864 h 125 25 cm h = 6 911 = 7 cm h 7 cm 10 cm

  45. (c) diagram. A field has shape and measurements as shown in the 35 m 30 m 85 m 80 m 120 35 50 m 80 30 120 m (i) Find, in metres, the length of the perimeter of the field. Perimeter = 80 + 120 + 50 + 85+ 30 + 35 m = 400 m

  46. (c) diagram. A field has shape and measurements as shown in the 35 m 30 m 80 m 50 m 120 m (ii) Find, in m2, the area of the field. Area = 35 30 + 50 120 = 1050 + 6000 = 7050 m2

  47. (c) diagram. A field has shape and measurements as shown in the 35 m 30 m 80 m Area = 7050 m2 Area =7050 10000 50 m _____ = 0 705 hectares 120 m (iii) Tim bought the field at a cost of 41 000 per hectare. How much did Tim pay for the field? [1 hectare = 10 000 m2] Cost = 0 705 41000 = 28 905

  48. (b) A bicycle wheel has a diameter of 60cm. (i) Calculate, in cm, the radius of the bicycle wheel. 1 Radius = diameter 2 60 = 30 cm (ii) Taking as 3 142 calculate, in cm, the circumference of the wheel. . Circumference = 2 r = 2 3 142 30 60 cm 30 cm = 188 52 cm

  49. (b) A bicycle wheel has a diameter of 60cm. (iii) How far does the bicycle travel when the wheel makes 340 complete turns? Give your answer to the nearest metre. One complete turn = 188 52 cm 340 complete turns = 188 52 340 1 metre = 100 cm 64096 cm m 8 100 = = 640 968 m = 641 m

  50. (c) (i) A rectangular piece of silver measures 4 cm by 24 cm. Find, in cm2, the area of the piece of silver. 24 cm 4 cm Area = length breadth = 24 4 = 96 cm2 (ii) Brian wants to cut circular discs of radius 2 cm from the piece of silver. What is the greatest number of discs that he can cut from the piece? Diameter = 2 2 = 4 cm Number of discs =24 2 cm = 6 4

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