Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 429 · 40 questions

How to solve it (Divide by 7 first): Circle: circumference = 2 × π × r; area = π × r × r. With π = 22/7, divide the radius by 7 first. Cube of edge a: volume = a × a × a, surface area = 6 × a × a. Cuboid: volume = l × b × h, surface area = 2 × (lb + bh + hl). Make every length k times as long: areas become k × k times as big, volumes k × k × k times.

1. 1.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
2. 2.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
3. 3.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 3 times (c) 9 times (d) 6 times
4. 4.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
5. 5.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 18 sq cm (b) 42 sq cm (c) 21 sq cm (d) 84 sq cm
6. 6.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 2 times (c) 8 times (d) 5 times
7. 7.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
8. 8.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 6 cu cm (c) 16 cu cm (d) 8 cu cm
9. 9.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 4 times (c) 16 times (d) 8 times
10. 10.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
11. 11.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 220 cm (d) 3850 cm
12. 12.A cuboid is 10 cm long, 9 cm wide and 4 cm high. What is its volume? (a) 23 cu cm (b) 90 cu cm (c) 360 cu cm (d) 332 cu cm
13. 13.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
14. 14.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 15 cu cm (b) 60 cu cm (c) 112 cu cm (d) 6 cu cm
15. 15.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 44 sq cm (d) 616 sq cm
16. 16.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 6 cu cm (b) 92 cu cm (c) 13 cu cm (d) 48 cu cm
17. 17.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 100 cu cm (c) 125 cu cm (d) 150 cu cm
18. 18.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
19. 19.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
20. 20.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 44 sq cm (d) 616 sq cm
21. 21.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 88 cm (d) 2464 cm
22. 22.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
23. 23.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 88 cm (d) 44 cm
24. 24.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 9 times (c) 6 times (d) 27 times
25. 25.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 4 sq cm (c) 24 sq cm (d) 8 sq cm
26. 26.A cuboid is 12 cm long, 10 cm wide and 2 cm high. What is its volume? (a) 24 cu cm (b) 328 cu cm (c) 240 cu cm (d) 120 cu cm
27. 27.A cube has edges of 5 cm. What is its total surface area? (a) 150 sq cm (b) 125 sq cm (c) 25 sq cm (d) 100 sq cm
28. 28.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 30 sq cm (b) 62 sq cm (c) 31 sq cm (d) 124 sq cm
29. 29.A cuboid is 10 cm long, 5 cm wide and 2 cm high. What is its total surface area? (a) 320 sq cm (b) 160 sq cm (c) 100 sq cm (d) 80 sq cm
30. 30.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 6 times (c) 4 times (d) 8 times
31. 31.A cuboid is 8 cm long, 5 cm wide and 6 cm high. What is its volume? (a) 19 cu cm (b) 236 cu cm (c) 240 cu cm (d) 40 cu cm
32. 32.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 88 sq cm
33. 33.A cuboid is 8 cm long, 5 cm wide and 4 cm high. What is its total surface area? (a) 184 sq cm (b) 92 sq cm (c) 368 sq cm (d) 160 sq cm
34. 34.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 25 times (c) 5 times (d) 125 times
35. 35.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 64 cu cm (b) 10 cu cm (c) 32 cu cm (d) 8 cu cm
36. 36.A cube has edges of 6 cm. What is its total surface area? (a) 36 sq cm (b) 144 sq cm (c) 216 sq cm (d) 217 sq cm
37. 37.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 54 cu cm (b) 14 cu cm (c) 6 cu cm (d) 102 cu cm
38. 38.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 176 cm (d) 88 cm
39. 39.A cube has edges of 4 cm. What is its volume? (a) 64 cu cm (b) 65 cu cm (c) 96 cu cm (d) 12 cu cm
40. 40.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm

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