Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 984 · 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 radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq 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) 10 times (c) 25 times (d) 125 times
3. 3.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 264 cm (d) 66 cm
4. 4.A cuboid is 5 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 80 sq cm (b) 264 sq cm (c) 132 sq cm (d) 66 sq cm
5. 5.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 4 times (c) 16 times (d) 64 times
6. 6.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 693 sq cm
7. 7.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
8. 8.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 1728 cu cm (c) 36 cu cm (d) 864 cu cm
9. 9.A cuboid is 5 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 96 sq cm (b) 20 sq cm (c) 48 sq cm (d) 24 sq cm
10. 10.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) 4 times (c) 8 times (d) 64 times
11. 11.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 144 sq cm (c) 864 sq cm (d) 1728 sq cm
12. 12.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
13. 13.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
14. 14.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 5 times (c) 8 times (d) 4 times
15. 15.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 176 cm (d) 616 cm
16. 16.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) 64 times (c) 8 times (d) 4 times
17. 17.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
18. 18.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
19. 19.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 2 times (c) 4 times (d) 6 times
20. 20.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) 8 times (c) 2 times (d) 4 times
21. 21.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
22. 22.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 176 sq cm
23. 23.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 54 sq cm (c) 36 sq cm (d) 9 sq cm
24. 24.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 176 cm (d) 88 cm
25. 25.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 729 sq cm (c) 486 sq cm (d) 324 sq cm
26. 26.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 220 cm (d) 3850 cm
27. 27.A cuboid is 6 cm long, 4 cm wide and 6 cm high. What is its total surface area? (a) 84 sq cm (b) 144 sq cm (c) 168 sq cm (d) 336 sq cm
28. 28.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
29. 29.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 88 cm (d) 22 cm
30. 30.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 21 sq cm (b) 84 sq cm (c) 42 sq cm (d) 18 sq cm
31. 31.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 36 cu cm (c) 54 cu cm (d) 9 cu cm
32. 32.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) 64 times (c) 4 times (d) 16 times
33. 33.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
34. 34.A cuboid is 6 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 18 cu cm (b) 184 cu cm (c) 12 cu cm (d) 120 cu cm
35. 35.A cube has edges of 4 cm. What is its total surface area? (a) 96 sq cm (b) 97 sq cm (c) 16 sq cm (d) 64 sq cm
36. 36.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
37. 37.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
38. 38.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 18 cu cm (c) 216 cu cm (d) 144 cu cm
39. 39.A cuboid is 6 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 360 sq cm (b) 144 sq cm (c) 180 sq cm (d) 90 sq cm
40. 40.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 294 sq cm (c) 49 sq cm (d) 343 sq cm

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