Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 364 · 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 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) 6 times (c) 3 times (d) 9 times
2. 2.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 132 sq cm
3. 3.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 3850 cm (d) 440 cm
4. 4.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
5. 5.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 121 sq cm (c) 484 sq cm (d) 726 sq cm
6. 6.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
7. 7.A cuboid is 9 cm long, 8 cm wide and 10 cm high. What is its total surface area? (a) 242 sq cm (b) 968 sq cm (c) 484 sq cm (d) 720 sq cm
8. 8.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
9. 9.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm
10. 10.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 5 times (c) 125 times (d) 25 times
11. 11.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 64 times (c) 4 times (d) 8 times
12. 12.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 112 cu cm (b) 6 cu cm (c) 60 cu cm (d) 15 cu cm
13. 13.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 66 cm (d) 264 cm
14. 14.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
15. 15.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) 3 times (d) 27 times
16. 16.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
17. 17.A cube has edges of 10 cm. What is its total surface area? (a) 400 sq cm (b) 100 sq cm (c) 1000 sq cm (d) 600 sq cm
18. 18.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) 8 times (c) 4 times (d) 5 times
19. 19.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 24 sq cm (c) 4 sq cm (d) 8 sq cm
20. 20.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 54 sq cm (c) 27 sq cm (d) 36 sq cm
21. 21.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 27 cu cm (c) 9 cu cm (d) 54 cu cm
22. 22.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
23. 23.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 6 times (c) 4 times (d) 8 times
24. 24.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 12 cu cm (c) 96 cu cm (d) 64 cu cm
25. 25.A cube has edges of 9 cm. What is its volume? (a) 486 cu cm (b) 324 cu cm (c) 729 cu cm (d) 27 cu cm
26. 26.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 125 cu cm (c) 150 cu cm (d) 100 cu cm
27. 27.A cuboid is 10 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 17 cu cm (b) 160 cu cm (c) 100 cu cm (d) 20 cu cm
28. 28.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 77 sq cm (d) 616 sq cm
29. 29.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) 9 times (d) 27 times
30. 30.A cuboid is 10 cm long, 9 cm wide and 8 cm high. What is its volume? (a) 27 cu cm (b) 484 cu cm (c) 720 cu cm (d) 90 cu cm
31. 31.A cuboid is 6 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 240 cu cm (b) 20 cu cm (c) 24 cu cm (d) 248 cu cm
32. 32.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
33. 33.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
34. 34.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
35. 35.A cuboid is 12 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 312 sq cm (b) 288 sq cm (c) 624 sq cm (d) 156 sq cm
36. 36.A cuboid is 11 cm long, 4 cm wide and 5 cm high. What is its total surface area? (a) 476 sq cm (b) 119 sq cm (c) 238 sq cm (d) 220 sq cm
37. 37.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
38. 38.A cuboid is 10 cm long, 6 cm wide and 10 cm high. What is its volume? (a) 440 cu cm (b) 26 cu cm (c) 600 cu cm (d) 60 cu cm
39. 39.A cuboid is 11 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 44 cu cm (b) 440 cu cm (c) 25 cu cm (d) 388 cu cm
40. 40.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

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