Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 721 · 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 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 44 cm (d) 616 cm
2. 2.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
3. 3.A cuboid is 6 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 240 cu cm (b) 24 cu cm (c) 20 cu cm (d) 248 cu cm
4. 4.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
5. 5.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 10 times (c) 125 times (d) 5 times
6. 6.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
7. 7.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 88 cm (d) 2464 cm
8. 8.A cuboid is 4 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 50 sq cm (b) 56 sq cm (c) 100 sq cm (d) 200 sq cm
9. 9.A cube has edges of 5 cm. What is its volume? (a) 100 cu cm (b) 150 cu cm (c) 15 cu cm (d) 125 cu cm
10. 10.A cuboid is 6 cm long, 5 cm wide and 5 cm high. What is its total surface area? (a) 85 sq cm (b) 340 sq cm (c) 150 sq cm (d) 170 sq cm
11. 11.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 3850 cm (d) 440 cm
12. 12.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 88 sq cm (d) 2464 sq cm
13. 13.A cuboid is 9 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 540 sq cm (b) 270 sq cm (c) 135 sq cm (d) 243 sq cm
14. 14.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
15. 15.A cuboid is 7 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 28 cu cm (b) 64 cu cm (c) 14 cu cm (d) 11 cu cm
16. 16.A cube has edges of 10 cm. What is its total surface area? (a) 100 sq cm (b) 600 sq cm (c) 400 sq cm (d) 1000 sq cm
17. 17.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
18. 18.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) 4 times (c) 8 times (d) 16 times
19. 19.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 64 times (c) 16 times (d) 8 times
20. 20.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 693 sq cm (d) 5544 sq cm
21. 21.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) 5 times (c) 8 times (d) 4 times
22. 22.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) 27 times (d) 3 times
23. 23.A cube has edges of 4 cm. What is its volume? (a) 64 cu cm (b) 12 cu cm (c) 65 cu cm (d) 96 cu cm
24. 24.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
25. 25.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
26. 26.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 44 sq cm (d) 154 sq cm
27. 27.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 54 sq cm (c) 27 sq cm (d) 9 sq cm
28. 28.A cuboid is 7 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 14 cu cm (b) 42 cu cm (c) 12 cu cm (d) 82 cu cm
29. 29.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 16 sq cm (b) 32 sq cm (c) 64 sq cm (d) 12 sq cm
30. 30.A cuboid is 10 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 15 cu cm (b) 20 cu cm (c) 60 cu cm (d) 112 cu cm
31. 31.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
32. 32.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
33. 33.A cuboid is 6 cm long, 5 cm wide and 3 cm high. What is its volume? (a) 90 cu cm (b) 14 cu cm (c) 30 cu cm (d) 126 cu cm
34. 34.A cuboid is 6 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 12 cu cm (b) 72 cu cm (c) 36 cu cm (d) 11 cu cm
35. 35.A cuboid is 12 cm long, 8 cm wide and 9 cm high. What is its volume? (a) 864 cu cm (b) 552 cu cm (c) 96 cu cm (d) 29 cu cm
36. 36.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) 6 times (c) 3 times (d) 9 times
37. 37.A cuboid is 12 cm long, 5 cm wide and 7 cm high. What is its total surface area? (a) 179 sq cm (b) 358 sq cm (c) 420 sq cm (d) 716 sq cm
38. 38.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 486 cu cm (c) 27 cu cm (d) 729 cu cm
39. 39.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
40. 40.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 14 cu cm (b) 6 cu cm (c) 54 cu cm (d) 102 cu cm

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