Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 467 · 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 6 cm. What is its total surface area? (a) 217 sq cm (b) 144 sq cm (c) 36 sq cm (d) 216 sq cm
2. 2.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
3. 3.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
4. 4.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) 125 times (c) 10 times (d) 25 times
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.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
7. 7.A cuboid is 5 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 180 sq cm (b) 45 sq cm (c) 90 sq cm (d) 50 sq cm
8. 8.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 9856 sq cm
9. 9.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 44 sq cm (d) 77 sq cm
10. 10.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
11. 11.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) 8 times (c) 64 times (d) 4 times
12. 12.If the radius of a circle 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
13. 13.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
14. 14.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
15. 15.A cuboid is 9 cm long, 8 cm wide and 9 cm high. What is its total surface area? (a) 450 sq cm (b) 900 sq cm (c) 225 sq cm (d) 648 sq cm
16. 16.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 176 cm (d) 44 cm
17. 17.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
18. 18.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 56 sq cm (b) 60 sq cm (c) 224 sq cm (d) 112 sq cm
19. 19.A cube has edges of 11 cm. What is its total surface area? (a) 726 sq cm (b) 121 sq cm (c) 1331 sq cm (d) 484 sq cm
20. 20.A cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 100 sq cm (c) 1000 sq cm (d) 400 sq cm
21. 21.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 8 times (c) 2 times (d) 6 times
22. 22.If the side of a square 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
23. 23.A cuboid is 7 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 98 cu cm (b) 154 cu cm (c) 16 cu cm (d) 14 cu cm
24. 24.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 616 cm (d) 44 cm
25. 25.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 10 times (c) 125 times (d) 5 times
26. 26.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 220 cm (d) 440 cm
27. 27.A cuboid is 11 cm long, 8 cm wide and 8 cm high. What is its total surface area? (a) 704 sq cm (b) 480 sq cm (c) 240 sq cm (d) 960 sq cm
28. 28.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 729 sq cm (c) 81 sq cm (d) 486 sq cm
29. 29.A cuboid is 10 cm long, 5 cm wide and 6 cm high. What is its total surface area? (a) 140 sq cm (b) 560 sq cm (c) 300 sq cm (d) 280 sq cm
30. 30.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 6 cu cm (c) 8 cu cm (d) 24 cu cm
31. 31.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
32. 32.A cuboid is 4 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 300 sq cm (b) 108 sq cm (c) 150 sq cm (d) 75 sq cm
33. 33.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
34. 34.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 54 sq cm (c) 36 sq cm (d) 27 sq cm
35. 35.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 2 times (d) 5 times
36. 36.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
37. 37.A cuboid is 5 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 38 sq cm (b) 76 sq cm (c) 152 sq cm (d) 40 sq cm
38. 38.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
39. 39.A cube has edges of 12 cm. What is its total surface area? (a) 144 sq cm (b) 576 sq cm (c) 864 sq cm (d) 1728 sq cm
40. 40.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm

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