Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 425 · 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 radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm
2. 2.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 264 cm (d) 66 cm
3. 3.A cuboid is 11 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 20 cu cm (b) 234 cu cm (c) 33 cu cm (d) 198 cu cm
4. 4.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
5. 5.A cuboid is 6 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 72 cu cm (b) 18 cu cm (c) 11 cu cm (d) 36 cu 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.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
8. 8.A cube has edges of 12 cm. What is its volume? (a) 1728 cu cm (b) 576 cu cm (c) 36 cu cm (d) 864 cu cm
9. 9.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 440 cm (d) 110 cm
10. 10.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
11. 11.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 150 cu cm (c) 100 cu cm (d) 15 cu cm
12. 12.A cube has edges of 10 cm. What is its volume? (a) 30 cu cm (b) 1000 cu cm (c) 400 cu cm (d) 600 cu cm
13. 13.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 9856 sq cm
14. 14.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm
15. 15.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
16. 16.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) 6 times (c) 3 times (d) 27 times
17. 17.A cube has edges of 11 cm. What is its total surface area? (a) 121 sq cm (b) 484 sq cm (c) 726 sq cm (d) 1331 sq cm
18. 18.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 729 cu cm (c) 27 cu cm (d) 486 cu cm
19. 19.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
20. 20.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
21. 21.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
22. 22.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
23. 23.A cuboid is 9 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 190 sq cm (b) 126 sq cm (c) 95 sq cm (d) 380 sq cm
24. 24.A cube has edges of 2 cm. What is its total surface area? (a) 4 sq cm (b) 8 sq cm (c) 16 sq cm (d) 24 sq cm
25. 25.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 125 times (c) 5 times (d) 25 times
26. 26.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 2 times (c) 8 times (d) 6 times
27. 27.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
28. 28.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
29. 29.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 132 sq cm
30. 30.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
31. 31.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
32. 32.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
33. 33.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 96 cu cm (c) 65 cu cm (d) 64 cu cm
34. 34.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
35. 35.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 16 sq cm (b) 12 sq cm (c) 32 sq cm (d) 64 sq cm
36. 36.A cuboid is 12 cm long, 11 cm wide and 4 cm high. What is its total surface area? (a) 224 sq cm (b) 528 sq cm (c) 896 sq cm (d) 448 sq cm
37. 37.A cube has edges of 12 cm. What is its total surface area? (a) 144 sq cm (b) 864 sq cm (c) 576 sq cm (d) 1728 sq cm
38. 38.A cuboid is 5 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 94 cu cm (b) 60 cu cm (c) 12 cu cm (d) 20 cu cm
39. 39.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 44 sq cm (d) 77 sq cm
40. 40.A cuboid is 9 cm long, 4 cm wide and 3 cm high. What is its total surface area? (a) 300 sq cm (b) 150 sq cm (c) 75 sq cm (d) 108 sq cm

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