Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 206 · 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 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
2. 2.A cube has edges of 5 cm. What is its volume? (a) 100 cu cm (b) 125 cu cm (c) 150 cu cm (d) 15 cu cm
3. 3.A cuboid is 11 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 304 cu cm (b) 23 cu cm (c) 220 cu cm (d) 22 cu cm
4. 4.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 110 cm (d) 440 cm
5. 5.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 88 cm (d) 154 cm
6. 6.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
7. 7.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) 25 times (c) 5 times (d) 10 times
8. 8.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 1232 sq cm
9. 9.A cube has edges of 7 cm. What is its total surface area? (a) 49 sq cm (b) 196 sq cm (c) 343 sq cm (d) 294 sq cm
10. 10.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
11. 11.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
12. 12.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 132 sq cm
13. 13.A cube has edges of 8 cm. What is its total surface area? (a) 384 sq cm (b) 512 sq cm (c) 256 sq cm (d) 64 sq cm
14. 14.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 4 times (c) 2 times (d) 8 times
15. 15.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 6 cu cm (c) 24 cu cm (d) 8 cu cm
16. 16.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 616 cm (d) 176 cm
17. 17.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 616 cm (d) 176 cm
18. 18.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
19. 19.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 12 sq cm (b) 64 sq cm (c) 16 sq cm (d) 32 sq cm
20. 20.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) 16 times (c) 64 times (d) 8 times
21. 21.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 616 sq cm
22. 22.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 144 cu cm (c) 217 cu cm (d) 216 cu cm
23. 23.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 5 times (c) 25 times (d) 125 times
24. 24.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 97 sq cm (c) 64 sq cm (d) 96 sq cm
25. 25.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) 9 times (d) 3 times
26. 26.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 308 sq cm
27. 27.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) 66 sq cm (d) 36 sq cm
28. 28.A cuboid is 8 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 96 cu cm (b) 97 cu cm (c) 16 cu cm (d) 152 cu cm
29. 29.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) 4 times (c) 2 times (d) 8 times
30. 30.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) 25 times (c) 125 times (d) 10 times
31. 31.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 60 sq cm (b) 112 sq cm (c) 56 sq cm (d) 224 sq cm
32. 32.A cuboid is 10 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 20 cu cm (b) 112 cu cm (c) 15 cu cm (d) 60 cu cm
33. 33.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
34. 34.A cuboid is 9 cm long, 5 cm wide and 2 cm high. What is its total surface area? (a) 90 sq cm (b) 292 sq cm (c) 73 sq cm (d) 146 sq cm
35. 35.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
36. 36.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
37. 37.A cuboid is 8 cm long, 6 cm wide and 5 cm high. What is its volume? (a) 240 cu cm (b) 236 cu cm (c) 48 cu cm (d) 19 cu cm
38. 38.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 176 cm (d) 88 cm
39. 39.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 132 sq cm (d) 5544 sq cm
40. 40.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) 9 times (c) 3 times (d) 6 times

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