Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 971 · 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 total surface area? (a) 100 sq cm (b) 125 sq cm (c) 25 sq cm (d) 150 sq cm
2. 2.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 400 cu cm (c) 1000 cu cm (d) 30 cu cm
3. 3.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
4. 4.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 56 sq cm (b) 224 sq cm (c) 60 sq cm (d) 112 sq cm
5. 5.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) 3 times (d) 9 times
6. 6.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
7. 7.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 5 times (c) 10 times (d) 125 times
8. 8.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
9. 9.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 9 times (c) 3 times (d) 27 times
10. 10.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 8 times (c) 4 times (d) 2 times
11. 11.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
12. 12.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
13. 13.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
14. 14.A cuboid is 11 cm long, 6 cm wide and 2 cm high. What is its volume? (a) 66 cu cm (b) 19 cu cm (c) 200 cu cm (d) 132 cu cm
15. 15.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 72 cu cm (b) 11 cu cm (c) 6 cu cm (d) 36 cu cm
16. 16.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
17. 17.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 100 cu cm (c) 15 cu cm (d) 125 cu cm
18. 18.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 352 cm (d) 176 cm
19. 19.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 1232 sq cm
20. 20.A cuboid is 5 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 80 cu cm (b) 132 cu cm (c) 15 cu cm (d) 10 cu cm
21. 21.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) 125 times (c) 5 times (d) 10 times
22. 22.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 9 sq cm (c) 36 sq cm (d) 54 sq cm
23. 23.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) 16 times (c) 64 times (d) 4 times
24. 24.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
25. 25.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 6 cu cm (c) 8 cu cm (d) 24 cu cm
26. 26.A cuboid is 10 cm long, 7 cm wide and 5 cm high. What is its total surface area? (a) 620 sq cm (b) 350 sq cm (c) 310 sq cm (d) 155 sq cm
27. 27.A cuboid is 5 cm long, 4 cm wide and 3 cm high. What is its total surface area? (a) 47 sq cm (b) 188 sq cm (c) 94 sq cm (d) 60 sq cm
28. 28.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) 125 times (c) 25 times (d) 10 times
29. 29.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
30. 30.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
31. 31.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 21 sq cm (b) 18 sq cm (c) 84 sq cm (d) 42 sq cm
32. 32.A cuboid is 6 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 18 cu cm (b) 108 cu cm (c) 15 cu cm (d) 144 cu cm
33. 33.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
34. 34.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 30 cu cm (b) 62 cu cm (c) 6 cu cm (d) 10 cu cm
35. 35.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) 8 times (c) 16 times (d) 4 times
36. 36.A cuboid is 11 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 173 sq cm (b) 346 sq cm (c) 330 sq cm (d) 692 sq cm
37. 37.A cube has edges of 6 cm. What is its total surface area? (a) 217 sq cm (b) 216 sq cm (c) 36 sq cm (d) 144 sq cm
38. 38.A cuboid is 8 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 86 sq cm (b) 112 sq cm (c) 344 sq cm (d) 172 sq cm
39. 39.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) 9 times (c) 3 times (d) 27 times
40. 40.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

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