Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 677 · 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.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 1386 cm (d) 66 cm
2. 2.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) 27 times (c) 3 times (d) 9 times
3. 3.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
4. 4.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
5. 5.A cuboid is 5 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 10 cu cm (b) 48 cu cm (c) 9 cu cm (d) 20 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.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 616 sq cm (d) 88 sq cm
8. 8.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 24 cu cm (c) 384 cu cm (d) 256 cu cm
9. 9.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 6 times (c) 8 times (d) 4 times
10. 10.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 4 sq cm (c) 8 sq cm (d) 24 sq cm
11. 11.A cube has edges of 6 cm. What is its volume? (a) 144 cu cm (b) 216 cu cm (c) 18 cu cm (d) 217 cu cm
12. 12.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
13. 13.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
14. 14.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 64 sq cm (c) 96 sq cm (d) 16 sq cm
15. 15.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 176 sq cm
16. 16.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 27 sq cm (c) 9 sq cm (d) 54 sq cm
17. 17.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
18. 18.A cuboid is 4 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 132 sq cm (b) 33 sq cm (c) 36 sq cm (d) 66 sq cm
19. 19.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 294 cu cm (c) 343 cu cm (d) 21 cu cm
20. 20.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 3850 cm (d) 110 cm
21. 21.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
22. 22.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) 3 times (c) 27 times (d) 6 times
23. 23.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 36 sq cm (c) 216 sq cm (d) 217 sq cm
24. 24.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) 16 times (c) 8 times (d) 4 times
25. 25.A cuboid is 7 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 444 sq cm (b) 222 sq cm (c) 189 sq cm (d) 111 sq cm
26. 26.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 36 cu cm (c) 864 cu cm (d) 1728 cu cm
27. 27.A cuboid is 7 cm long, 5 cm wide and 8 cm high. What is its volume? (a) 262 cu cm (b) 20 cu cm (c) 280 cu cm (d) 35 cu cm
28. 28.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
29. 29.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) 3 times (c) 6 times (d) 27 times
30. 30.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
31. 31.A cuboid is 10 cm long, 7 cm wide and 2 cm high. What is its total surface area? (a) 140 sq cm (b) 208 sq cm (c) 104 sq cm (d) 416 sq cm
32. 32.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 2 times (d) 5 times
33. 33.A cuboid is 5 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 15 cu cm (b) 13 cu cm (c) 75 cu cm (d) 110 cu cm
34. 34.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 5 times (c) 2 times (d) 8 times
35. 35.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 8 cu cm (c) 16 cu cm (d) 6 cu cm
36. 36.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
37. 37.A cuboid is 9 cm long, 8 cm wide and 3 cm high. What is its volume? (a) 216 cu cm (b) 246 cu cm (c) 72 cu cm (d) 20 cu cm
38. 38.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 10 times (c) 25 times (d) 5 times
39. 39.A cuboid is 4 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 150 sq cm (b) 108 sq cm (c) 75 sq cm (d) 300 sq cm
40. 40.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm

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