Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 133 · 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 cuboid is 6 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 188 cu cm (b) 168 cu cm (c) 24 cu cm (d) 17 cu cm
2. 2.A cube has edges of 10 cm. What is its volume? (a) 30 cu cm (b) 400 cu cm (c) 1000 cu cm (d) 600 cu cm
3. 3.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
4. 4.A cube has edges of 5 cm. What is its volume? (a) 100 cu cm (b) 15 cu cm (c) 125 cu cm (d) 150 cu cm
5. 5.A cuboid is 5 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 200 cu cm (b) 220 cu cm (c) 20 cu cm (d) 19 cu cm
6. 6.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
7. 7.A cuboid is 9 cm long, 5 cm wide and 2 cm high. What is its volume? (a) 45 cu cm (b) 146 cu cm (c) 90 cu cm (d) 16 cu cm
8. 8.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) 64 times (c) 4 times (d) 8 times
9. 9.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 616 cm (d) 176 cm
10. 10.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm
11. 11.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
12. 12.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
13. 13.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 44 cm (d) 616 cm
14. 14.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) 6 times (c) 9 times (d) 3 times
15. 15.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 12 cu cm (c) 96 cu cm (d) 64 cu cm
16. 16.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 6 times (c) 27 times (d) 9 times
17. 17.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
18. 18.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 440 cm (d) 220 cm
19. 19.A cuboid is 10 cm long, 8 cm wide and 7 cm high. What is its volume? (a) 25 cu cm (b) 412 cu cm (c) 560 cu cm (d) 80 cu cm
20. 20.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 4 times (c) 8 times (d) 16 times
21. 21.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 1232 sq cm
22. 22.A cuboid is 11 cm long, 8 cm wide and 7 cm high. What is its volume? (a) 26 cu cm (b) 88 cu cm (c) 442 cu cm (d) 616 cu cm
23. 23.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 1386 cm (d) 264 cm
24. 24.A cuboid is 5 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 174 cu cm (b) 135 cu cm (c) 17 cu cm (d) 15 cu cm
25. 25.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
26. 26.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
27. 27.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 21 cu cm (c) 196 cu cm (d) 343 cu cm
28. 28.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 4 times (c) 2 times (d) 5 times
29. 29.A cuboid is 7 cm long, 5 cm wide and 4 cm high. What is its total surface area? (a) 83 sq cm (b) 140 sq cm (c) 166 sq cm (d) 332 sq cm
30. 30.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 8 cu cm (c) 6 cu cm (d) 24 cu cm
31. 31.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
32. 32.A cuboid is 7 cm long, 6 cm wide and 3 cm high. What is its volume? (a) 42 cu cm (b) 162 cu cm (c) 16 cu cm (d) 126 cu cm
33. 33.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
34. 34.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 729 sq cm (c) 324 sq cm (d) 486 sq cm
35. 35.A cuboid is 8 cm long, 6 cm wide and 6 cm high. What is its total surface area? (a) 288 sq cm (b) 528 sq cm (c) 132 sq cm (d) 264 sq cm
36. 36.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
37. 37.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) 125 times (c) 10 times (d) 25 times
38. 38.A cuboid is 12 cm long, 11 cm wide and 10 cm high. What is its volume? (a) 132 cu cm (b) 1320 cu cm (c) 33 cu cm (d) 724 cu cm
39. 39.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 125 sq cm (c) 150 sq cm (d) 25 sq cm
40. 40.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm

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