Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 759 · 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 cuboid is 12 cm long, 8 cm wide and 3 cm high. What is its volume? (a) 23 cu cm (b) 96 cu cm (c) 312 cu cm (d) 288 cu cm
2. 2.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
3. 3.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) 25 times (c) 125 times (d) 10 times
4. 4.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) 8 times (c) 2 times (d) 5 times
5. 5.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 88 cm (d) 44 cm
6. 6.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 110 cm (d) 3850 cm
7. 7.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
8. 8.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
9. 9.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 24 sq cm (c) 16 sq cm (d) 4 sq cm
10. 10.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
11. 11.A cuboid is 9 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 124 cu cm (b) 15 cu cm (c) 18 cu cm (d) 72 cu cm
12. 12.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
13. 13.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 44 sq cm (d) 616 sq cm
14. 14.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 9856 sq cm
15. 15.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
16. 16.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
17. 17.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 112 sq cm (b) 60 sq cm (c) 56 sq cm (d) 224 sq cm
18. 18.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) 27 times (c) 6 times (d) 3 times
19. 19.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm
20. 20.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 6 times (c) 27 times (d) 9 times
21. 21.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
22. 22.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 3 times (c) 6 times (d) 27 times
23. 23.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 384 cu cm (c) 24 cu cm (d) 512 cu cm
24. 24.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
25. 25.A cuboid is 5 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 152 sq cm (b) 38 sq cm (c) 40 sq cm (d) 76 sq cm
26. 26.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
27. 27.A cuboid is 4 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 272 sq cm (b) 80 sq cm (c) 136 sq cm (d) 68 sq cm
28. 28.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 352 cm (d) 176 cm
29. 29.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 2 times (c) 6 times (d) 4 times
30. 30.A cube has edges of 5 cm. What is its volume? (a) 100 cu cm (b) 150 cu cm (c) 125 cu cm (d) 15 cu cm
31. 31.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 27 cu cm (c) 36 cu cm (d) 54 cu cm
32. 32.A cuboid is 9 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 222 sq cm (b) 189 sq cm (c) 111 sq cm (d) 444 sq cm
33. 33.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
34. 34.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 36 sq cm (c) 54 sq cm (d) 9 sq cm
35. 35.A cuboid is 5 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 100 cu cm (b) 10 cu cm (c) 17 cu cm (d) 160 cu cm
36. 36.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm
37. 37.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) 8 times (c) 16 times (d) 4 times
38. 38.A cube has edges of 11 cm. What is its volume? (a) 1331 cu cm (b) 484 cu cm (c) 33 cu cm (d) 726 cu cm
39. 39.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) 27 times (c) 9 times (d) 6 times
40. 40.A cube has edges of 6 cm. What is its total surface area? (a) 217 sq cm (b) 36 sq cm (c) 216 sq cm (d) 144 sq cm

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