Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 454 · 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 5 cm. What is its volume? (a) 150 cu cm (b) 15 cu cm (c) 125 cu cm (d) 100 cu cm
2. 2.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 176 cm (d) 44 cm
3. 3.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 6 cu cm (c) 16 cu cm (d) 24 cu cm
4. 4.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
5. 5.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
6. 6.A cuboid is 4 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 150 sq cm (b) 300 sq cm (c) 75 sq cm (d) 108 sq cm
7. 7.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 27 times (c) 6 times (d) 3 times
8. 8.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
9. 9.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
10. 10.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 512 cu cm (c) 24 cu cm (d) 384 cu cm
11. 11.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) 25 times (d) 10 times
12. 12.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
13. 13.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 176 sq cm
14. 14.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
15. 15.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 3 times (c) 9 times (d) 6 times
16. 16.A cuboid is 8 cm long, 4 cm wide and 8 cm high. What is its total surface area? (a) 256 sq cm (b) 512 sq cm (c) 257 sq cm (d) 128 sq cm
17. 17.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) 4 times (d) 8 times
18. 18.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
19. 19.A cuboid is 7 cm long, 6 cm wide and 9 cm high. What is its total surface area? (a) 318 sq cm (b) 378 sq cm (c) 159 sq cm (d) 636 sq cm
20. 20.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
21. 21.A cuboid is 11 cm long, 10 cm wide and 3 cm high. What is its volume? (a) 24 cu cm (b) 330 cu cm (c) 110 cu cm (d) 346 cu cm
22. 22.A cuboid is 7 cm long, 5 cm wide and 5 cm high. What is its volume? (a) 190 cu cm (b) 175 cu cm (c) 17 cu cm (d) 35 cu cm
23. 23.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
24. 24.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) 27 times (c) 6 times (d) 9 times
25. 25.A cuboid is 9 cm long, 6 cm wide and 5 cm high. What is its volume? (a) 54 cu cm (b) 258 cu cm (c) 20 cu cm (d) 270 cu cm
26. 26.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 2464 cm (d) 88 cm
27. 27.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
28. 28.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 6 times (c) 27 times (d) 3 times
29. 29.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
30. 30.A cuboid is 9 cm long, 6 cm wide and 5 cm high. What is its total surface area? (a) 516 sq cm (b) 270 sq cm (c) 258 sq cm (d) 129 sq cm
31. 31.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 54 cu cm (c) 9 cu cm (d) 36 cu cm
32. 32.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
33. 33.A cuboid is 5 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 94 cu cm (b) 20 cu cm (c) 60 cu cm (d) 12 cu cm
34. 34.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 16 times (c) 64 times (d) 4 times
35. 35.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 9856 sq cm
36. 36.A cuboid is 11 cm long, 6 cm wide and 3 cm high. What is its volume? (a) 66 cu cm (b) 234 cu cm (c) 20 cu cm (d) 198 cu cm
37. 37.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
38. 38.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 4 times (c) 8 times (d) 5 times
39. 39.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 3850 cm (d) 440 cm
40. 40.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 96 sq cm (c) 16 sq cm (d) 97 sq cm

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