Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 85 · 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 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 22 cm (d) 154 cm
2. 2.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) 25 times (c) 125 times (d) 10 times
3. 3.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
4. 4.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 400 cu cm (c) 1000 cu cm (d) 30 cu cm
5. 5.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 88 cm (d) 2464 cm
6. 6.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 3 times (c) 9 times (d) 6 times
7. 7.A cuboid is 5 cm long, 4 cm wide and 5 cm high. What is its volume? (a) 130 cu cm (b) 14 cu cm (c) 100 cu cm (d) 20 cu cm
8. 8.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 44 sq cm (d) 77 sq cm
9. 9.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 1232 sq cm
10. 10.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 256 cu cm (c) 512 cu cm (d) 24 cu cm
11. 11.A cuboid is 9 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 222 cu cm (b) 189 cu cm (c) 27 cu cm (d) 19 cu cm
12. 12.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 16 times (c) 64 times (d) 4 times
13. 13.A cube has edges of 4 cm. What is its total surface area? (a) 96 sq cm (b) 16 sq cm (c) 64 sq cm (d) 97 sq cm
14. 14.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
15. 15.A cuboid is 11 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 206 sq cm (b) 412 sq cm (c) 103 sq cm (d) 165 sq cm
16. 16.A cuboid is 5 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 94 cu cm (b) 20 cu cm (c) 12 cu cm (d) 60 cu cm
17. 17.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
18. 18.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
19. 19.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 64 cu cm (c) 12 cu cm (d) 65 cu cm
20. 20.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 616 sq cm
21. 21.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
22. 22.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 30 cu cm (b) 10 cu cm (c) 6 cu cm (d) 62 cu cm
23. 23.A cuboid is 9 cm long, 7 cm wide and 2 cm high. What is its volume? (a) 63 cu cm (b) 18 cu cm (c) 190 cu cm (d) 126 cu cm
24. 24.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 9 times (c) 27 times (d) 3 times
25. 25.A cuboid is 10 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 242 sq cm (b) 484 sq cm (c) 121 sq cm (d) 210 sq cm
26. 26.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) 8 times (c) 64 times (d) 4 times
27. 27.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
28. 28.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
29. 29.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 217 cu cm (c) 144 cu cm (d) 216 cu cm
30. 30.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
31. 31.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) 10 times (c) 25 times (d) 125 times
32. 32.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 8 times (c) 4 times (d) 16 times
33. 33.A cuboid is 5 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 30 cu cm (b) 10 cu cm (c) 62 cu cm (d) 15 cu cm
34. 34.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 12 cu cm (b) 42 cu cm (c) 82 cu cm (d) 6 cu cm
35. 35.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 21 cu cm (c) 294 cu cm (d) 343 cu cm
36. 36.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 726 cu cm (c) 1331 cu cm (d) 33 cu cm
37. 37.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 125 times (c) 25 times (d) 5 times
38. 38.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 343 sq cm (c) 49 sq cm (d) 294 sq cm
39. 39.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
40. 40.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 16 cu cm (c) 6 cu cm (d) 8 cu cm

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