Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 145 · 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 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
2. 2.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
3. 3.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
4. 4.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) 27 times (d) 6 times
5. 5.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 6 times (c) 27 times (d) 3 times
6. 6.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
7. 7.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 36 cu cm (c) 1728 cu cm (d) 864 cu cm
8. 8.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
9. 9.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
10. 10.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq cm
11. 11.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 384 cu cm (c) 256 cu cm (d) 512 cu cm
12. 12.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 6 times (c) 2 times (d) 8 times
13. 13.A cuboid is 5 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 135 cu cm (b) 174 cu cm (c) 15 cu cm (d) 17 cu cm
14. 14.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 33 cu cm (c) 726 cu cm (d) 1331 cu cm
15. 15.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
16. 16.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) 10 times (c) 25 times (d) 125 times
17. 17.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
18. 18.A cuboid is 7 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 98 sq cm (b) 154 sq cm (c) 308 sq cm (d) 77 sq cm
19. 19.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) 8 times (d) 16 times
20. 20.A cube has edges of 11 cm. What is its total surface area? (a) 484 sq cm (b) 726 sq cm (c) 1331 sq cm (d) 121 sq cm
21. 21.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) 8 times (d) 2 times
22. 22.A cuboid is 12 cm long, 9 cm wide and 5 cm high. What is its total surface area? (a) 540 sq cm (b) 213 sq cm (c) 426 sq cm (d) 852 sq cm
23. 23.A cube has edges of 7 cm. What is its total surface area? (a) 49 sq cm (b) 343 sq cm (c) 196 sq cm (d) 294 sq cm
24. 24.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
25. 25.A cuboid is 12 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 324 sq cm (b) 684 sq cm (c) 171 sq cm (d) 342 sq cm
26. 26.A cuboid is 9 cm long, 6 cm wide and 2 cm high. What is its total surface area? (a) 84 sq cm (b) 108 sq cm (c) 168 sq cm (d) 336 sq cm
27. 27.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 64 cu cm (c) 96 cu cm (d) 12 cu cm
28. 28.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 440 cm (d) 110 cm
29. 29.A cuboid is 5 cm long, 4 cm wide and 4 cm high. What is its total surface area? (a) 80 sq cm (b) 224 sq cm (c) 112 sq cm (d) 56 sq cm
30. 30.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
31. 31.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 110 cm (d) 440 cm
32. 32.A cuboid is 7 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 56 sq cm (b) 100 sq cm (c) 200 sq cm (d) 50 sq cm
33. 33.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm
34. 34.A cube has edges of 10 cm. What is its volume? (a) 400 cu cm (b) 1000 cu cm (c) 30 cu cm (d) 600 cu cm
35. 35.A cube has edges of 5 cm. What is its total surface area? (a) 150 sq cm (b) 25 sq cm (c) 100 sq cm (d) 125 sq cm
36. 36.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 22 cm (d) 44 cm
37. 37.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
38. 38.A cuboid is 12 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 108 cu cm (b) 36 cu cm (c) 162 cu cm (d) 18 cu cm
39. 39.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 44 sq cm (d) 77 sq cm
40. 40.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm

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