Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 840 · 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 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
2. 2.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 6 times (c) 27 times (d) 9 times
3. 3.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
4. 4.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 5 times (c) 4 times (d) 2 times
5. 5.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 10 times (c) 25 times (d) 125 times
6. 6.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 110 cm (d) 440 cm
7. 7.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 176 sq cm
8. 8.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 64 times (d) 16 times
9. 9.A cuboid is 7 cm long, 3 cm wide and 10 cm high. What is its volume? (a) 21 cu cm (b) 210 cu cm (c) 20 cu cm (d) 242 cu cm
10. 10.A cuboid is 6 cm long, 5 cm wide and 10 cm high. What is its volume? (a) 30 cu cm (b) 21 cu cm (c) 280 cu cm (d) 300 cu cm
11. 11.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 220 cm (d) 440 cm
12. 12.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 384 sq cm (c) 256 sq cm (d) 512 sq cm
13. 13.A cuboid is 6 cm long, 4 cm wide and 5 cm high. What is its total surface area? (a) 74 sq cm (b) 148 sq cm (c) 296 sq cm (d) 120 sq cm
14. 14.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 9856 sq cm
15. 15.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
16. 16.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 176 cm (d) 88 cm
17. 17.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
18. 18.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 24 cu cm (c) 16 cu cm (d) 6 cu cm
19. 19.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
20. 20.A cuboid is 11 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 88 sq cm (b) 148 sq cm (c) 74 sq cm (d) 296 sq cm
21. 21.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
22. 22.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 217 cu cm (c) 216 cu cm (d) 144 cu cm
23. 23.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
24. 24.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 6 cu cm (b) 36 cu cm (c) 11 cu cm (d) 72 cu cm
25. 25.A cuboid is 11 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 66 cu cm (b) 22 cu cm (c) 16 cu cm (d) 122 cu cm
26. 26.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) 5 times (c) 2 times (d) 8 times
27. 27.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
28. 28.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 51 sq cm (b) 54 sq cm (c) 102 sq cm (d) 204 sq cm
29. 29.A cuboid is 6 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 216 sq cm (b) 114 sq cm (c) 228 sq cm (d) 456 sq cm
30. 30.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 132 sq cm
31. 31.A cuboid is 5 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 220 sq cm (b) 110 sq cm (c) 440 sq cm (d) 200 sq cm
32. 32.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 3 times (c) 9 times (d) 6 times
33. 33.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 729 sq cm (c) 486 sq cm (d) 324 sq cm
34. 34.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
35. 35.A cuboid is 9 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 243 cu cm (b) 27 cu cm (c) 21 cu cm (d) 270 cu cm
36. 36.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 6 times (c) 9 times (d) 3 times
37. 37.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 64 times (c) 4 times (d) 16 times
38. 38.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 144 sq cm (c) 217 sq cm (d) 36 sq cm
39. 39.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
40. 40.A cuboid is 6 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 48 sq cm (b) 176 sq cm (c) 88 sq cm (d) 44 sq cm

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