Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 221 · 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 diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
2. 2.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 616 sq cm
3. 3.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
4. 4.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
5. 5.A cuboid is 8 cm long, 7 cm wide and 2 cm high. What is its volume? (a) 17 cu cm (b) 56 cu cm (c) 172 cu cm (d) 112 cu cm
6. 6.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
7. 7.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 8 times (c) 64 times (d) 4 times
8. 8.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 12 cu cm (b) 6 cu cm (c) 42 cu cm (d) 82 cu cm
9. 9.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
10. 10.A cube has edges of 6 cm. What is its total surface area? (a) 36 sq cm (b) 217 sq cm (c) 216 sq cm (d) 144 sq cm
11. 11.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
12. 12.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 2 times (c) 8 times (d) 4 times
13. 13.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
14. 14.A cube has edges of 11 cm. What is its total surface area? (a) 121 sq cm (b) 484 sq cm (c) 726 sq cm (d) 1331 sq cm
15. 15.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) 8 times (c) 2 times (d) 5 times
16. 16.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
17. 17.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 176 cm (d) 88 cm
18. 18.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
19. 19.A cuboid is 5 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 76 sq cm (b) 152 sq cm (c) 40 sq cm (d) 38 sq cm
20. 20.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
21. 21.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) 16 times (d) 64 times
22. 22.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 9 cu cm (b) 24 cu cm (c) 52 cu cm (d) 6 cu cm
23. 23.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) 16 times (c) 8 times (d) 4 times
24. 24.A cuboid is 5 cm long, 4 cm wide and 7 cm high. What is its total surface area? (a) 83 sq cm (b) 166 sq cm (c) 332 sq cm (d) 140 sq cm
25. 25.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 294 cu cm (c) 343 cu cm (d) 196 cu cm
26. 26.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 14 cu cm (b) 102 cu cm (c) 54 cu cm (d) 6 cu cm
27. 27.A cuboid is 5 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 70 sq cm (b) 118 sq cm (c) 59 sq cm (d) 236 sq cm
28. 28.A cuboid is 8 cm long, 4 cm wide and 9 cm high. What is its volume? (a) 21 cu cm (b) 32 cu cm (c) 280 cu cm (d) 288 cu cm
29. 29.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
30. 30.A cuboid is 11 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 33 cu cm (b) 22 cu cm (c) 264 cu cm (d) 290 cu cm
31. 31.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 24 cu cm (c) 512 cu cm (d) 256 cu cm
32. 32.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
33. 33.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 25 sq cm (c) 125 sq cm (d) 150 sq cm
34. 34.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 10 times (c) 5 times (d) 25 times
35. 35.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
36. 36.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
37. 37.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 5 times (c) 8 times (d) 2 times
38. 38.A cube has edges of 4 cm. What is its total surface area? (a) 96 sq cm (b) 97 sq cm (c) 64 sq cm (d) 16 sq cm
39. 39.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
40. 40.A cube has edges of 7 cm. What is its total surface area? (a) 294 sq cm (b) 49 sq cm (c) 196 sq cm (d) 343 sq cm

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