Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 457 · 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 2 cm. What is its total surface area? (a) 16 sq cm (b) 24 sq cm (c) 8 sq cm (d) 4 sq cm
2. 2.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
3. 3.A cuboid is 11 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 103 sq cm (b) 165 sq cm (c) 412 sq cm (d) 206 sq cm
4. 4.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 693 sq cm
5. 5.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
6. 6.A cube has edges of 9 cm. What is its total surface area? (a) 486 sq cm (b) 81 sq cm (c) 729 sq cm (d) 324 sq cm
7. 7.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 44 cm (d) 176 cm
8. 8.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 30 cu cm (c) 400 cu cm (d) 600 cu cm
9. 9.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
10. 10.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 264 cm (d) 1386 cm
11. 11.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 97 sq cm (c) 96 sq cm (d) 64 sq cm
12. 12.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) 25 times (c) 125 times (d) 10 times
13. 13.A cuboid is 5 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 10 cu cm (b) 90 cu cm (c) 12 cu cm (d) 50 cu cm
14. 14.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 27 times (c) 6 times (d) 3 times
15. 15.A cuboid is 4 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 164 sq cm (b) 82 sq cm (c) 120 sq cm (d) 328 sq cm
16. 16.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
17. 17.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
18. 18.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
19. 19.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 4 times (c) 8 times (d) 5 times
20. 20.A cuboid is 4 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 188 sq cm (b) 94 sq cm (c) 60 sq cm (d) 47 sq cm
21. 21.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
22. 22.A cuboid is 7 cm long, 5 cm wide and 7 cm high. What is its total surface area? (a) 119 sq cm (b) 245 sq cm (c) 238 sq cm (d) 476 sq cm
23. 23.A cuboid is 12 cm long, 9 cm wide and 2 cm high. What is its volume? (a) 23 cu cm (b) 216 cu cm (c) 108 cu cm (d) 300 cu cm
24. 24.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 308 sq cm
25. 25.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) 9 times (c) 3 times (d) 6 times
26. 26.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 22 cm (d) 88 cm
27. 27.A cube has edges of 3 cm. What is its total surface area? (a) 54 sq cm (b) 36 sq cm (c) 9 sq cm (d) 27 sq cm
28. 28.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 65 cu cm (c) 64 cu cm (d) 12 cu cm
29. 29.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
30. 30.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) 64 times (c) 8 times (d) 16 times
31. 31.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
32. 32.A cube has edges of 12 cm. What is its total surface area? (a) 144 sq cm (b) 864 sq cm (c) 1728 sq cm (d) 576 sq cm
33. 33.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 8 times (c) 4 times (d) 2 times
34. 34.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 308 sq cm
35. 35.A cuboid is 10 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 332 sq cm (b) 360 sq cm (c) 166 sq cm (d) 664 sq cm
36. 36.A cuboid is 6 cm long, 4 cm wide and 3 cm high. What is its total surface area? (a) 54 sq cm (b) 216 sq cm (c) 72 sq cm (d) 108 sq cm
37. 37.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
38. 38.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 42 cu cm (b) 82 cu cm (c) 12 cu cm (d) 6 cu cm
39. 39.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) 16 times (c) 64 times (d) 4 times
40. 40.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) 5 times (c) 25 times (d) 125 times

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