Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 765 · 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 radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 64 times (c) 4 times (d) 16 times
2. 2.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) 2 times (c) 5 times (d) 8 times
3. 3.If the side of a square 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
4. 4.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 64 times (c) 16 times (d) 4 times
5. 5.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
6. 6.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
7. 7.If the side of a square 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
8. 8.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 264 cm (d) 66 cm
9. 9.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
10. 10.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
11. 11.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
12. 12.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
13. 13.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
14. 14.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 24 cu cm (c) 512 cu cm (d) 256 cu cm
15. 15.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
16. 16.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
17. 17.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 44 sq cm (d) 77 sq cm
18. 18.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
19. 19.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) 25 times (c) 10 times (d) 125 times
20. 20.A cube has edges of 11 cm. What is its volume? (a) 726 cu cm (b) 1331 cu cm (c) 33 cu cm (d) 484 cu cm
21. 21.A cuboid is 5 cm long, 4 cm wide and 6 cm high. What is its total surface area? (a) 148 sq cm (b) 74 sq cm (c) 296 sq cm (d) 120 sq cm
22. 22.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 12 cu cm (b) 6 cu cm (c) 82 cu cm (d) 42 cu cm
23. 23.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
24. 24.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
25. 25.A cube has edges of 9 cm. What is its total surface area? (a) 486 sq cm (b) 324 sq cm (c) 81 sq cm (d) 729 sq cm
26. 26.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 864 cu cm (c) 1728 cu cm (d) 36 cu cm
27. 27.A cuboid is 10 cm long, 9 cm wide and 9 cm high. What is its total surface area? (a) 810 sq cm (b) 1044 sq cm (c) 261 sq cm (d) 522 sq cm
28. 28.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
29. 29.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 44 sq cm (d) 77 sq cm
30. 30.A cuboid is 9 cm long, 4 cm wide and 8 cm high. What is its total surface area? (a) 560 sq cm (b) 280 sq cm (c) 288 sq cm (d) 140 sq cm
31. 31.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) 25 times (c) 10 times (d) 5 times
32. 32.A cuboid is 6 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 90 cu cm (b) 12 cu cm (c) 54 cu cm (d) 18 cu cm
33. 33.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
34. 34.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
35. 35.A cube has edges of 10 cm. What is its volume? (a) 400 cu cm (b) 30 cu cm (c) 600 cu cm (d) 1000 cu cm
36. 36.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 8 times (c) 64 times (d) 16 times
37. 37.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
38. 38.A cuboid is 10 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 16 cu cm (b) 80 cu cm (c) 20 cu cm (d) 136 cu cm
39. 39.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
40. 40.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 100 cu cm (c) 125 cu cm (d) 150 cu cm

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