Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 398 · 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 circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
2. 2.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) 4 times (c) 2 times (d) 5 times
3. 3.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
4. 4.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 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) 9 times (b) 6 times (c) 27 times (d) 3 times
6. 6.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) 2 times (d) 4 times
7. 7.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) 10 times (c) 5 times (d) 25 times
8. 8.A cube has edges of 11 cm. What is its volume? (a) 726 cu cm (b) 33 cu cm (c) 1331 cu cm (d) 484 cu cm
9. 9.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
10. 10.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
11. 11.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
12. 12.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
13. 13.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
14. 14.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 24 sq cm (c) 4 sq cm (d) 16 sq cm
15. 15.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
16. 16.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 132 cm (d) 1386 cm
17. 17.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
18. 18.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
19. 19.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
20. 20.A cube has edges of 7 cm. What is its total surface area? (a) 49 sq cm (b) 343 sq cm (c) 294 sq cm (d) 196 sq cm
21. 21.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
22. 22.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
23. 23.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm
24. 24.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 125 sq cm (c) 150 sq cm (d) 25 sq cm
25. 25.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 256 cu cm (c) 512 cu cm (d) 384 cu cm
26. 26.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 77 sq cm (d) 44 sq cm
27. 27.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 400 cu cm (c) 30 cu cm (d) 1000 cu cm
28. 28.A cuboid is 4 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 76 sq cm (b) 40 sq cm (c) 152 sq cm (d) 38 sq cm
29. 29.A cuboid is 8 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 404 sq cm (b) 101 sq cm (c) 168 sq cm (d) 202 sq cm
30. 30.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 3 times (c) 9 times (d) 6 times
31. 31.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
32. 32.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
33. 33.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 486 sq cm (c) 81 sq cm (d) 324 sq cm
34. 34.A cuboid is 9 cm long, 5 cm wide and 3 cm high. What is its volume? (a) 45 cu cm (b) 17 cu cm (c) 174 cu cm (d) 135 cu cm
35. 35.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 9 sq cm (c) 54 sq cm (d) 36 sq cm
36. 36.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 12 cu cm (c) 64 cu cm (d) 96 cu 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) 4 times (c) 16 times (d) 8 times
38. 38.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 176 cm (d) 88 cm
39. 39.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) 4 times (c) 16 times (d) 64 times
40. 40.A cuboid is 4 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 120 sq cm (b) 164 sq cm (c) 328 sq cm (d) 82 sq cm

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