Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 275 · 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 diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
2. 2.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
3. 3.A cuboid is 5 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 60 cu cm (b) 10 cu cm (c) 13 cu cm (d) 104 cu cm
4. 4.A cuboid is 7 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 112 sq cm (b) 172 sq cm (c) 86 sq cm (d) 344 sq cm
5. 5.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
6. 6.A cube has edges of 7 cm. What is its total surface area? (a) 343 sq cm (b) 196 sq cm (c) 49 sq cm (d) 294 sq cm
7. 7.A cuboid is 9 cm long, 4 cm wide and 9 cm high. What is its volume? (a) 306 cu cm (b) 36 cu cm (c) 324 cu cm (d) 22 cu cm
8. 8.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 3850 cm (d) 110 cm
9. 9.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
10. 10.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 3 times (c) 6 times (d) 27 times
11. 11.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 102 cu cm (b) 6 cu cm (c) 54 cu cm (d) 14 cu cm
12. 12.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
13. 13.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
14. 14.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
15. 15.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
16. 16.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
17. 17.A cuboid is 6 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 16 cu cm (b) 96 cu cm (c) 152 cu cm (d) 12 cu cm
18. 18.A cuboid is 7 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 28 sq cm (b) 128 sq cm (c) 32 sq cm (d) 64 sq cm
19. 19.A cube has edges of 2 cm. What is its total surface area? (a) 4 sq cm (b) 24 sq cm (c) 8 sq cm (d) 16 sq cm
20. 20.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 2 times (d) 5 times
21. 21.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 352 cm (d) 88 cm
22. 22.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 9856 sq cm
23. 23.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
24. 24.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
25. 25.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 216 cu cm (c) 144 cu cm (d) 18 cu cm
26. 26.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 36 sq cm (c) 54 sq cm (d) 27 sq cm
27. 27.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 16 times (c) 64 times (d) 8 times
28. 28.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) 9 times (d) 27 times
29. 29.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 729 cu cm (c) 486 cu cm (d) 324 cu cm
30. 30.A cuboid is 10 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 332 sq cm (b) 166 sq cm (c) 360 sq cm (d) 664 sq cm
31. 31.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) 8 times (c) 4 times (d) 16 times
32. 32.A cuboid is 8 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 76 sq cm (b) 96 sq cm (c) 304 sq cm (d) 152 sq cm
33. 33.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 616 sq cm
34. 34.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 384 sq cm (c) 256 sq cm (d) 64 sq cm
35. 35.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
36. 36.A cuboid is 11 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 100 sq cm (b) 400 sq cm (c) 132 sq cm (d) 200 sq cm
37. 37.A cuboid is 8 cm long, 5 cm wide and 10 cm high. What is its volume? (a) 340 cu cm (b) 40 cu cm (c) 23 cu cm (d) 400 cu cm
38. 38.A cuboid is 12 cm long, 11 cm wide and 8 cm high. What is its total surface area? (a) 632 sq cm (b) 316 sq cm (c) 1264 sq cm (d) 1056 sq cm
39. 39.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 88 cm (d) 352 cm
40. 40.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 8 times (d) 4 times

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