Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 506 · 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.A cuboid is 11 cm long, 8 cm wide and 6 cm high. What is its volume? (a) 88 cu cm (b) 528 cu cm (c) 404 cu cm (d) 25 cu cm
2. 2.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 616 cm (d) 176 cm
3. 3.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 4 times (c) 8 times (d) 2 times
4. 4.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) 125 times (c) 25 times (d) 10 times
5. 5.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
6. 6.A cuboid is 5 cm long, 4 cm wide and 5 cm high. What is its volume? (a) 100 cu cm (b) 130 cu cm (c) 14 cu cm (d) 20 cu cm
7. 7.A cube has edges of 4 cm. What is its volume? (a) 64 cu cm (b) 96 cu cm (c) 12 cu cm (d) 65 cu cm
8. 8.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 256 cu cm (c) 24 cu cm (d) 512 cu cm
9. 9.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
10. 10.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 1386 cm (d) 66 cm
11. 11.A cuboid is 5 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 208 sq cm (b) 104 sq cm (c) 60 sq cm (d) 52 sq cm
12. 12.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 2464 cm (d) 352 cm
13. 13.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 15 cu cm (c) 100 cu cm (d) 125 cu cm
14. 14.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
15. 15.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 4 times (c) 64 times (d) 8 times
16. 16.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 66 cm (d) 1386 cm
17. 17.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
18. 18.A cube has edges of 9 cm. What is its total surface area? (a) 486 sq cm (b) 81 sq cm (c) 729 sq cm (d) 324 sq cm
19. 19.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
20. 20.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
21. 21.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
22. 22.A cube has edges of 10 cm. What is its total surface area? (a) 1000 sq cm (b) 400 sq cm (c) 100 sq cm (d) 600 sq cm
23. 23.A cuboid is 10 cm long, 6 cm wide and 2 cm high. What is its total surface area? (a) 184 sq cm (b) 92 sq cm (c) 368 sq cm (d) 120 sq cm
24. 24.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 44 sq cm (d) 154 sq cm
25. 25.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
26. 26.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 1728 cu cm (c) 36 cu cm (d) 864 cu cm
27. 27.A cuboid is 12 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 108 sq cm (b) 81 sq cm (c) 162 sq cm (d) 324 sq cm
28. 28.A cube has edges of 11 cm. What is its total surface area? (a) 121 sq cm (b) 1331 sq cm (c) 484 sq cm (d) 726 sq cm
29. 29.A cube has edges of 6 cm. What is its volume? (a) 216 cu cm (b) 144 cu cm (c) 18 cu cm (d) 217 cu cm
30. 30.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 1728 sq cm (c) 864 sq cm (d) 144 sq cm
31. 31.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 308 sq cm (d) 2464 sq cm
32. 32.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) 16 times (c) 8 times (d) 4 times
33. 33.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
34. 34.A cube has edges of 9 cm. What is its volume? (a) 486 cu cm (b) 324 cu cm (c) 27 cu cm (d) 729 cu cm
35. 35.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) 27 times (c) 3 times (d) 9 times
36. 36.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
37. 37.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
38. 38.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) 125 times (c) 25 times (d) 5 times
39. 39.A cuboid is 8 cm long, 7 cm wide and 5 cm high. What is its volume? (a) 20 cu cm (b) 280 cu cm (c) 262 cu cm (d) 56 cu cm
40. 40.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 36 sq cm (c) 9 sq cm (d) 54 sq cm

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