Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 883 · 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 3 times as long, how many times as big does its area become? (a) 6 times (b) 9 times (c) 27 times (d) 3 times
2. 2.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 352 cm (d) 2464 cm
3. 3.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) 9 times (c) 27 times (d) 3 times
4. 4.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 1232 sq cm
5. 5.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
6. 6.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 1232 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) 64 times (b) 4 times (c) 8 times (d) 16 times
8. 8.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
9. 9.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) 5 times (c) 8 times (d) 2 times
10. 10.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
11. 11.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
12. 12.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
13. 13.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) 5 times (d) 4 times
14. 14.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
15. 15.A cuboid is 9 cm long, 7 cm wide and 4 cm high. What is its total surface area? (a) 508 sq cm (b) 252 sq cm (c) 127 sq cm (d) 254 sq cm
16. 16.A cuboid is 9 cm long, 7 cm wide and 7 cm high. What is its total surface area? (a) 175 sq cm (b) 700 sq cm (c) 350 sq cm (d) 441 sq cm
17. 17.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
18. 18.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
19. 19.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 44 sq cm (d) 616 sq cm
20. 20.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 16 cu cm (c) 8 cu cm (d) 24 cu cm
21. 21.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
22. 22.A cube has edges of 9 cm. What is its volume? (a) 486 cu cm (b) 324 cu cm (c) 27 cu cm (d) 729 cu cm
23. 23.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 125 times (c) 5 times (d) 10 times
24. 24.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
25. 25.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 8 times (c) 4 times (d) 2 times
26. 26.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
27. 27.A cuboid is 5 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 188 sq cm (b) 47 sq cm (c) 94 sq cm (d) 60 sq cm
28. 28.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 1386 cm (d) 66 cm
29. 29.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 88 cm (d) 44 cm
30. 30.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
31. 31.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) 4 times (c) 8 times (d) 16 times
32. 32.A cuboid is 4 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 80 cu cm (b) 136 cu cm (c) 8 cu cm (d) 16 cu cm
33. 33.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 4 sq cm (c) 16 sq cm (d) 24 sq cm
34. 34.A cuboid is 6 cm long, 5 cm wide and 4 cm high. What is its total surface area? (a) 120 sq cm (b) 148 sq cm (c) 296 sq cm (d) 74 sq cm
35. 35.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 25 sq cm (c) 125 sq cm (d) 150 sq cm
36. 36.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 125 times (c) 10 times (d) 5 times
37. 37.A cuboid is 5 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 45 sq cm (b) 39 sq cm (c) 156 sq cm (d) 78 sq cm
38. 38.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 27 cu cm (c) 54 cu cm (d) 36 cu cm
39. 39.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 10 times (c) 25 times (d) 125 times
40. 40.A cuboid is 4 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 76 cu cm (b) 8 cu cm (c) 40 cu cm (d) 11 cu cm

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