Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 125 · 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 4 cm. What is its volume? (a) 64 cu cm (b) 12 cu cm (c) 96 cu cm (d) 65 cu cm
2. 2.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
3. 3.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
4. 4.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
5. 5.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
6. 6.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) 16 times (c) 8 times (d) 4 times
7. 7.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 5 times (c) 25 times (d) 125 times
8. 8.A cuboid is 6 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 152 cu cm (b) 96 cu cm (c) 16 cu cm (d) 12 cu cm
9. 9.A cube has edges of 7 cm. What is its volume? (a) 343 cu cm (b) 21 cu cm (c) 196 cu cm (d) 294 cu cm
10. 10.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 616 cm (d) 176 cm
11. 11.A cube has edges of 11 cm. What is its volume? (a) 33 cu cm (b) 1331 cu cm (c) 484 cu cm (d) 726 cu cm
12. 12.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 125 sq cm (c) 100 sq cm (d) 150 sq cm
13. 13.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 100 cu cm (c) 150 cu cm (d) 15 cu cm
14. 14.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 6 times (c) 27 times (d) 9 times
15. 15.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
16. 16.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 864 sq cm (c) 144 sq cm (d) 1728 sq cm
17. 17.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 176 cm (d) 88 cm
18. 18.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 176 cm (d) 88 cm
19. 19.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 30 cu cm (c) 400 cu cm (d) 1000 cu cm
20. 20.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 4 times (c) 16 times (d) 8 times
21. 21.A cuboid is 4 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 76 sq cm (b) 152 sq cm (c) 40 sq cm (d) 38 sq cm
22. 22.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
23. 23.A cuboid is 10 cm long, 8 cm wide and 6 cm high. What is its total surface area? (a) 188 sq cm (b) 480 sq cm (c) 376 sq cm (d) 752 sq cm
24. 24.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 54 sq cm (c) 27 sq cm (d) 9 sq cm
25. 25.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
26. 26.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 44 sq cm (d) 154 sq cm
27. 27.A cuboid is 4 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 11 cu cm (b) 80 cu cm (c) 48 cu cm (d) 12 cu cm
28. 28.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
29. 29.A cuboid is 6 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 114 sq cm (b) 216 sq cm (c) 228 sq cm (d) 456 sq cm
30. 30.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
31. 31.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 132 cm (d) 1386 cm
32. 32.A cuboid is 4 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 11 cu cm (b) 76 cu cm (c) 8 cu cm (d) 40 cu cm
33. 33.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) 3 times (c) 6 times (d) 9 times
34. 34.A cuboid is 10 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 16 cu cm (b) 40 cu cm (c) 80 cu cm (d) 136 cu cm
35. 35.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 729 cu cm (c) 486 cu cm (d) 27 cu cm
36. 36.A cuboid is 4 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 300 sq cm (b) 75 sq cm (c) 150 sq cm (d) 108 sq 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) 25 times (d) 10 times
38. 38.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
39. 39.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) 6 times (c) 9 times (d) 3 times
40. 40.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 308 sq cm (d) 2464 sq cm

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