Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 881 · 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 radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 88 cm (d) 44 cm
2. 2.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
3. 3.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
4. 4.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) 9 times (c) 3 times (d) 6 times
5. 5.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 sq cm
6. 6.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq cm
7. 7.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 9 times (c) 3 times (d) 6 times
8. 8.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 10 times (d) 25 times
9. 9.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) 9 times (c) 27 times (d) 3 times
10. 10.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
11. 11.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 1386 sq cm
12. 12.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
13. 13.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 150 cu cm (c) 100 cu cm (d) 125 cu cm
14. 14.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
15. 15.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 440 cm (d) 220 cm
16. 16.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) 10 times (d) 25 times
17. 17.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 110 cm (d) 440 cm
18. 18.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
19. 19.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
20. 20.A cube has edges of 10 cm. What is its total surface area? (a) 1000 sq cm (b) 600 sq cm (c) 100 sq cm (d) 400 sq cm
21. 21.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) 3 times (d) 27 times
22. 22.A cuboid is 10 cm long, 9 cm wide and 4 cm high. What is its volume? (a) 23 cu cm (b) 360 cu cm (c) 90 cu cm (d) 332 cu cm
23. 23.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 150 sq cm (c) 100 sq cm (d) 125 sq cm
24. 24.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 5 times (c) 25 times (d) 125 times
25. 25.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 16 sq cm (b) 80 sq cm (c) 40 sq cm (d) 20 sq cm
26. 26.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
27. 27.A cuboid is 6 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 24 cu cm (b) 48 cu cm (c) 12 cu cm (d) 88 cu cm
28. 28.A cuboid is 10 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 14 cu cm (b) 20 cu cm (c) 88 cu cm (d) 40 cu cm
29. 29.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
30. 30.A cuboid is 4 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 12 cu cm (b) 88 cu cm (c) 48 cu cm (d) 8 cu cm
31. 31.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 729 cu cm (c) 324 cu cm (d) 486 cu cm
32. 32.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 22 cm (d) 88 cm
33. 33.A cuboid is 11 cm long, 5 cm wide and 9 cm high. What is its volume? (a) 495 cu cm (b) 398 cu cm (c) 25 cu cm (d) 55 cu cm
34. 34.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 144 sq cm (c) 1728 sq cm (d) 576 sq cm
35. 35.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
36. 36.A cuboid is 6 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 11 cu cm (b) 36 cu cm (c) 72 cu cm (d) 12 cu cm
37. 37.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) 2 times (c) 4 times (d) 6 times
38. 38.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 7 cu cm (b) 32 cu cm (c) 6 cu cm (d) 12 cu cm
39. 39.A cuboid is 11 cm long, 10 cm wide and 10 cm high. What is its total surface area? (a) 1280 sq cm (b) 320 sq cm (c) 1100 sq cm (d) 640 sq cm
40. 40.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 44 sq cm (d) 154 sq cm

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