Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 124 · 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 circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
2. 2.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 132 sq cm (d) 5544 sq cm
3. 3.A cuboid is 5 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 17 cu cm (b) 15 cu cm (c) 135 cu cm (d) 174 cu cm
4. 4.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
5. 5.A cuboid is 6 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 88 cu cm (b) 12 cu cm (c) 48 cu cm (d) 24 cu cm
6. 6.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 6 times (c) 9 times (d) 3 times
7. 7.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 1232 sq cm
8. 8.A cuboid is 7 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 101 sq cm (b) 168 sq cm (c) 202 sq cm (d) 404 sq cm
9. 9.A cube has edges of 3 cm. What is its total surface area? (a) 54 sq cm (b) 36 sq cm (c) 9 sq cm (d) 27 sq cm
10. 10.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 308 sq cm
11. 11.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
12. 12.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
13. 13.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times
14. 14.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 16 sq cm (c) 96 sq cm (d) 97 sq cm
15. 15.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
16. 16.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 264 cm (d) 66 cm
17. 17.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 4 times (c) 8 times (d) 64 times
18. 18.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
19. 19.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
20. 20.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm
21. 21.A cuboid is 11 cm long, 7 cm wide and 10 cm high. What is its total surface area? (a) 1028 sq cm (b) 257 sq cm (c) 514 sq cm (d) 770 sq cm
22. 22.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 64 cu cm (c) 12 cu cm (d) 96 cu cm
23. 23.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 264 cm (d) 1386 cm
24. 24.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
25. 25.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 6 times (c) 27 times (d) 3 times
26. 26.A cuboid is 9 cm long, 7 cm wide and 9 cm high. What is its volume? (a) 63 cu cm (b) 567 cu cm (c) 25 cu cm (d) 414 cu cm
27. 27.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
28. 28.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 22 cm (d) 154 cm
29. 29.A cuboid is 7 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 136 cu cm (b) 15 cu cm (c) 14 cu cm (d) 84 cu cm
30. 30.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 4 sq cm (c) 24 sq cm (d) 16 sq cm
31. 31.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 49 sq cm (c) 294 sq cm (d) 343 sq cm
32. 32.A cuboid is 7 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 140 cu cm (b) 208 cu cm (c) 19 cu cm (d) 14 cu cm
33. 33.A cube has edges of 10 cm. What is its volume? (a) 30 cu cm (b) 1000 cu cm (c) 400 cu cm (d) 600 cu cm
34. 34.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
35. 35.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 8 times (c) 5 times (d) 4 times
36. 36.A cuboid is 9 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 146 sq cm (b) 292 sq cm (c) 90 sq cm (d) 73 sq cm
37. 37.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 8 times (c) 64 times (d) 16 times
38. 38.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 112 cu cm (b) 60 cu cm (c) 6 cu cm (d) 15 cu cm
39. 39.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
40. 40.A cuboid is 8 cm long, 5 cm wide and 9 cm high. What is its total surface area? (a) 628 sq cm (b) 314 sq cm (c) 360 sq cm (d) 157 sq cm

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