Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 535 · 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 radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
2. 2.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 616 cm (d) 176 cm
3. 3.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 24 cu cm (c) 256 cu cm (d) 384 cu cm
4. 4.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
5. 5.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) 64 times (d) 16 times
6. 6.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
7. 7.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 96 sq cm (c) 97 sq cm (d) 64 sq cm
8. 8.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 132 cm (d) 1386 cm
9. 9.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
10. 10.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
11. 11.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
12. 12.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
13. 13.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 77 sq cm (d) 616 sq cm
14. 14.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 5 times (c) 10 times (d) 25 times
15. 15.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
16. 16.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm
17. 17.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 4 times (c) 64 times (d) 8 times
18. 18.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
19. 19.A cuboid is 5 cm long, 4 cm wide and 4 cm high. What is its total surface area? (a) 112 sq cm (b) 56 sq cm (c) 224 sq cm (d) 80 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) 5 times (b) 4 times (c) 8 times (d) 2 times
21. 21.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) 5 times (d) 2 times
22. 22.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
23. 23.A cube has edges of 7 cm. What is its total surface area? (a) 49 sq cm (b) 294 sq cm (c) 343 sq cm (d) 196 sq cm
24. 24.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
25. 25.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 616 sq cm
26. 26.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) 27 times (c) 6 times (d) 9 times
27. 27.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
28. 28.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
29. 29.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) 25 times (d) 5 times
30. 30.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 343 cu cm (c) 21 cu cm (d) 294 cu cm
31. 31.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 4 times (b) 2 times (c) 8 times (d) 5 times
32. 32.A cuboid is 9 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 108 cu cm (b) 27 cu cm (c) 150 cu cm (d) 16 cu cm
33. 33.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 125 times (c) 5 times (d) 10 times
34. 34.A cube has edges of 9 cm. What is its volume? (a) 486 cu cm (b) 27 cu cm (c) 324 cu cm (d) 729 cu cm
35. 35.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
36. 36.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 144 sq cm (c) 576 sq cm (d) 1728 sq cm
37. 37.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) 5 times (c) 25 times (d) 10 times
38. 38.A cube has edges of 6 cm. What is its total surface area? (a) 217 sq cm (b) 36 sq cm (c) 216 sq cm (d) 144 sq cm
39. 39.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) 4 times (d) 6 times
40. 40.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 100 cu cm (c) 125 cu cm (d) 15 cu cm

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