Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 96 · 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.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 4 times (d) 5 times
2. 2.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
3. 3.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) 16 times (c) 8 times (d) 4 times
4. 4.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 44 cm (d) 616 cm
5. 5.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
6. 6.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 81 sq cm (c) 486 sq cm (d) 324 sq cm
7. 7.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) 16 times (c) 64 times (d) 4 times
8. 8.If the radius of a circle 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
9. 9.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
10. 10.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
11. 11.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 1232 sq cm
12. 12.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 343 cu cm (c) 196 cu cm (d) 294 cu cm
13. 13.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
14. 14.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
15. 15.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
16. 16.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) 6 times (c) 2 times (d) 4 times
17. 17.A cube has edges of 9 cm. What is its volume? (a) 729 cu cm (b) 324 cu cm (c) 486 cu cm (d) 27 cu cm
18. 18.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
19. 19.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
20. 20.A cuboid is 4 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 72 sq cm (b) 216 sq cm (c) 108 sq cm (d) 54 sq cm
21. 21.A cuboid is 5 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 100 cu cm (b) 160 cu cm (c) 10 cu cm (d) 17 cu cm
22. 22.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
23. 23.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 6 cu cm (b) 48 cu cm (c) 13 cu cm (d) 92 cu cm
24. 24.A cuboid is 11 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 173 sq cm (b) 692 sq cm (c) 330 sq cm (d) 346 sq cm
25. 25.A cuboid is 4 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 47 sq cm (b) 188 sq cm (c) 60 sq cm (d) 94 sq cm
26. 26.A cuboid is 5 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 100 sq cm (b) 160 sq cm (c) 320 sq cm (d) 80 sq cm
27. 27.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 132 cm (d) 1386 cm
28. 28.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
29. 29.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 176 sq cm
30. 30.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
31. 31.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
32. 32.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) 27 times (c) 3 times (d) 6 times
33. 33.A cuboid is 12 cm long, 6 cm wide and 6 cm high. What is its total surface area? (a) 432 sq cm (b) 360 sq cm (c) 720 sq cm (d) 180 sq cm
34. 34.A cuboid is 4 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 112 cu cm (b) 8 cu cm (c) 64 cu cm (d) 14 cu cm
35. 35.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 125 cu cm (c) 100 cu cm (d) 15 cu cm
36. 36.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
37. 37.A cube has edges of 11 cm. What is its volume? (a) 1331 cu cm (b) 33 cu cm (c) 726 cu cm (d) 484 cu cm
38. 38.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 24 cu cm (c) 8 cu cm (d) 16 cu cm
39. 39.A cuboid is 7 cm long, 5 cm wide and 10 cm high. What is its volume? (a) 35 cu cm (b) 310 cu cm (c) 350 cu cm (d) 22 cu cm
40. 40.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 616 sq cm

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