Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 642 · 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 cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 400 sq cm (c) 100 sq cm (d) 1000 sq cm
2. 2.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 486 sq cm (c) 729 sq cm (d) 81 sq cm
3. 3.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
4. 4.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
5. 5.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 132 cm (d) 1386 cm
6. 6.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 125 cu cm (c) 15 cu cm (d) 100 cu cm
7. 7.A cuboid is 10 cm long, 5 cm wide and 2 cm high. What is its volume? (a) 160 cu cm (b) 17 cu cm (c) 50 cu cm (d) 100 cu cm
8. 8.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
9. 9.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
10. 10.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) 9 times (c) 27 times (d) 3 times
11. 11.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times
12. 12.A cuboid is 12 cm long, 5 cm wide and 2 cm high. What is its total surface area? (a) 188 sq cm (b) 376 sq cm (c) 120 sq cm (d) 94 sq cm
13. 13.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 308 sq cm
14. 14.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
15. 15.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 144 cu cm (c) 217 cu cm (d) 216 cu cm
16. 16.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 729 cu cm (c) 324 cu cm (d) 486 cu cm
17. 17.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
18. 18.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) 8 times (c) 6 times (d) 4 times
19. 19.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 125 times (b) 25 times (c) 10 times (d) 5 times
20. 20.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
21. 21.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 125 times (c) 10 times (d) 5 times
22. 22.A cube has edges of 7 cm. What is its volume? (a) 343 cu cm (b) 294 cu cm (c) 196 cu cm (d) 21 cu cm
23. 23.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
24. 24.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 3850 cm (d) 440 cm
25. 25.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
26. 26.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 384 sq cm (c) 512 sq cm (d) 256 sq cm
27. 27.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 9 cu cm (c) 54 cu cm (d) 27 cu cm
28. 28.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 8 cu cm (c) 24 cu cm (d) 16 cu cm
29. 29.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
30. 30.A cuboid is 12 cm long, 7 cm wide and 5 cm high. What is its volume? (a) 420 cu cm (b) 358 cu cm (c) 24 cu cm (d) 84 cu cm
31. 31.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
32. 32.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 352 cm (d) 2464 cm
33. 33.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
34. 34.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
35. 35.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) 27 times (c) 3 times (d) 6 times
36. 36.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
37. 37.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 125 times (c) 5 times (d) 25 times
38. 38.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 46 sq cm (b) 184 sq cm (c) 48 sq cm (d) 92 sq cm
39. 39.A cube has edges of 11 cm. What is its volume? (a) 1331 cu cm (b) 484 cu cm (c) 726 cu cm (d) 33 cu cm
40. 40.A cuboid is 8 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 112 cu cm (b) 32 cu cm (c) 14 cu cm (d) 64 cu cm

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