Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 637 · 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 8 cm. What is its volume? (a) 384 cu cm (b) 512 cu cm (c) 256 cu cm (d) 24 cu cm
2. 2.A cuboid is 9 cm long, 7 cm wide and 9 cm high. What is its volume? (a) 25 cu cm (b) 414 cu cm (c) 63 cu cm (d) 567 cu cm
3. 3.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 9 times (c) 27 times (d) 3 times
4. 4.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) 5 times (c) 4 times (d) 2 times
5. 5.A cuboid is 7 cm long, 5 cm wide and 10 cm high. What is its volume? (a) 350 cu cm (b) 35 cu cm (c) 22 cu cm (d) 310 cu cm
6. 6.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
7. 7.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 132 sq cm
8. 8.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
9. 9.If the radius of a circle 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
10. 10.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 6 times (c) 27 times (d) 9 times
11. 11.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 16 times (d) 8 times
12. 12.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
13. 13.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
14. 14.A cuboid is 9 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 36 cu cm (b) 15 cu cm (c) 124 cu cm (d) 72 cu cm
15. 15.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
16. 16.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 77 sq cm (d) 44 sq cm
17. 17.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm
18. 18.A cuboid is 9 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 14 cu cm (b) 27 cu cm (c) 54 cu cm (d) 102 cu cm
19. 19.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 264 cm (d) 66 cm
20. 20.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 10 times (c) 125 times (d) 25 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.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) 125 times (c) 10 times (d) 5 times
23. 23.A cuboid is 11 cm long, 5 cm wide and 8 cm high. What is its total surface area? (a) 732 sq cm (b) 440 sq cm (c) 366 sq cm (d) 183 sq cm
24. 24.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
25. 25.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 5 times (c) 10 times (d) 125 times
26. 26.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
27. 27.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 343 cu cm (c) 294 cu cm (d) 21 cu cm
28. 28.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 220 cm (d) 440 cm
29. 29.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
30. 30.A cuboid is 12 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 36 cu cm (b) 17 cu cm (c) 132 cu cm (d) 72 cu cm
31. 31.A cuboid is 7 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 18 cu cm (b) 190 cu cm (c) 126 cu cm (d) 14 cu cm
32. 32.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) 3 times (c) 6 times (d) 9 times
33. 33.A cuboid is 12 cm long, 5 cm wide and 2 cm high. What is its volume? (a) 60 cu cm (b) 188 cu cm (c) 120 cu cm (d) 19 cu cm
34. 34.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
35. 35.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
36. 36.A cuboid is 11 cm long, 6 cm wide and 3 cm high. What is its volume? (a) 20 cu cm (b) 234 cu cm (c) 198 cu cm (d) 66 cu cm
37. 37.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
38. 38.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 576 cu cm (c) 1728 cu cm (d) 36 cu cm
39. 39.A cuboid is 9 cm long, 6 cm wide and 7 cm high. What is its total surface area? (a) 378 sq cm (b) 636 sq cm (c) 318 sq cm (d) 159 sq cm
40. 40.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 150 sq cm (c) 125 sq cm (d) 25 sq cm

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