Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 92 · 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) 693 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 5544 sq cm
2. 2.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) 8 times (c) 16 times (d) 4 times
3. 3.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
4. 4.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 176 cm (d) 44 cm
5. 5.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 3 times (c) 9 times (d) 6 times
6. 6.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
7. 7.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 3850 cm (d) 440 cm
8. 8.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
9. 9.A cube has edges of 2 cm. What is its total surface area? (a) 4 sq cm (b) 16 sq cm (c) 24 sq cm (d) 8 sq cm
10. 10.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 9 cu cm (b) 24 cu cm (c) 6 cu cm (d) 52 cu cm
11. 11.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
12. 12.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) 27 times (c) 6 times (d) 3 times
13. 13.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
14. 14.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 8 times (c) 5 times (d) 4 times
15. 15.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) 6 times (c) 27 times (d) 3 times
16. 16.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 16 times (d) 64 times
17. 17.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
18. 18.A cube has edges of 10 cm. What is its total surface area? (a) 1000 sq cm (b) 400 sq cm (c) 600 sq cm (d) 100 sq cm
19. 19.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 5 times (c) 25 times (d) 10 times
20. 20.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 25 times (c) 10 times (d) 5 times
21. 21.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
22. 22.A cuboid is 4 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 112 cu cm (b) 64 cu cm (c) 14 cu cm (d) 8 cu cm
23. 23.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 9856 sq cm
24. 24.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
25. 25.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 27 cu cm (c) 486 cu cm (d) 729 cu cm
26. 26.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
27. 27.A cube has edges of 11 cm. What is its total surface area? (a) 484 sq cm (b) 1331 sq cm (c) 121 sq cm (d) 726 sq cm
28. 28.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
29. 29.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
30. 30.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
31. 31.A cuboid is 10 cm long, 9 cm wide and 7 cm high. What is its total surface area? (a) 223 sq cm (b) 892 sq cm (c) 630 sq cm (d) 446 sq cm
32. 32.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 21 cu cm (c) 196 cu cm (d) 343 cu cm
33. 33.A cuboid is 5 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 292 sq cm (b) 90 sq cm (c) 146 sq cm (d) 73 sq cm
34. 34.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
35. 35.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) 4 times (d) 2 times
36. 36.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 308 sq cm
37. 37.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) 4 times (c) 2 times (d) 8 times
38. 38.A cube has edges of 6 cm. What is its volume? (a) 216 cu cm (b) 18 cu cm (c) 144 cu cm (d) 217 cu cm
39. 39.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 384 cu cm (c) 24 cu cm (d) 256 cu cm
40. 40.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 264 cm (d) 1386 cm

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