Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 155 · 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 diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
2. 2.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) 64 times (c) 4 times (d) 16 times
3. 3.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq cm
4. 4.A cuboid is 11 cm long, 10 cm wide and 4 cm high. What is its total surface area? (a) 194 sq cm (b) 440 sq cm (c) 388 sq cm (d) 776 sq cm
5. 5.A cube has edges of 10 cm. What is its total surface area? (a) 100 sq cm (b) 400 sq cm (c) 1000 sq cm (d) 600 sq cm
6. 6.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 44 sq cm (d) 616 sq cm
7. 7.If the radius of a circle 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
8. 8.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 2464 cm (d) 352 cm
9. 9.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 11 cu cm (b) 6 cu cm (c) 72 cu cm (d) 36 cu cm
10. 10.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 294 cu cm (c) 343 cu cm (d) 196 cu cm
11. 11.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 15 cu cm (b) 6 cu cm (c) 60 cu cm (d) 112 cu cm
12. 12.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
13. 13.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 440 cm (d) 110 cm
14. 14.A cuboid is 10 cm long, 7 cm wide and 3 cm high. What is its volume? (a) 20 cu cm (b) 210 cu cm (c) 70 cu cm (d) 242 cu cm
15. 15.A cuboid is 4 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 120 sq cm (b) 328 sq cm (c) 82 sq cm (d) 164 sq cm
16. 16.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 6 times (c) 9 times (d) 3 times
17. 17.A cuboid is 7 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 210 cu cm (b) 28 cu cm (c) 18 cu cm (d) 196 cu cm
18. 18.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
19. 19.A cuboid is 9 cm long, 4 cm wide and 6 cm high. What is its total surface area? (a) 456 sq cm (b) 114 sq cm (c) 216 sq cm (d) 228 sq cm
20. 20.A cube has edges of 12 cm. What is its total surface area? (a) 144 sq cm (b) 576 sq cm (c) 1728 sq cm (d) 864 sq cm
21. 21.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 97 sq cm (c) 96 sq cm (d) 16 sq cm
22. 22.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
23. 23.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 693 sq cm
24. 24.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 8 cu cm (c) 6 cu cm (d) 16 cu cm
25. 25.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 144 cu cm (c) 216 cu cm (d) 18 cu cm
26. 26.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
27. 27.A cube has edges of 11 cm. What is its volume? (a) 726 cu cm (b) 484 cu cm (c) 33 cu cm (d) 1331 cu cm
28. 28.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
29. 29.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
30. 30.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 27 cu cm (c) 36 cu cm (d) 54 cu cm
31. 31.A cuboid is 6 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 96 sq cm (b) 76 sq cm (c) 152 sq cm (d) 304 sq cm
32. 32.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 44 cm (d) 616 cm
33. 33.A cuboid is 7 cm long, 6 cm wide and 3 cm high. What is its volume? (a) 42 cu cm (b) 16 cu cm (c) 126 cu cm (d) 162 cu cm
34. 34.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) 9 times (c) 27 times (d) 6 times
35. 35.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 384 cu cm (c) 512 cu cm (d) 24 cu cm
36. 36.A cuboid is 5 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 17 cu cm (b) 160 cu cm (c) 10 cu cm (d) 100 cu cm
37. 37.A cube has edges of 11 cm. What is its total surface area? (a) 484 sq cm (b) 121 sq cm (c) 1331 sq cm (d) 726 sq cm
38. 38.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
39. 39.A cuboid is 10 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 180 sq cm (b) 432 sq cm (c) 216 sq cm (d) 108 sq cm
40. 40.A cuboid is 12 cm long, 5 cm wide and 5 cm high. What is its volume? (a) 300 cu cm (b) 60 cu cm (c) 290 cu cm (d) 22 cu cm

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