Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 587 · 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 70 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 3850 cm (d) 110 cm
2. 2.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 125 cu cm (c) 15 cu cm (d) 100 cu cm
3. 3.A cuboid is 12 cm long, 6 cm wide and 6 cm high. What is its volume? (a) 432 cu cm (b) 72 cu cm (c) 24 cu cm (d) 360 cu cm
4. 4.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) 125 times (c) 25 times (d) 5 times
5. 5.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
6. 6.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 352 cm (d) 176 cm
7. 7.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
8. 8.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 16 sq cm (b) 64 sq cm (c) 12 sq cm (d) 32 sq cm
9. 9.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) 27 times (c) 3 times (d) 6 times
10. 10.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 5 times (d) 2 times
11. 11.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 25 times (c) 10 times (d) 125 times
12. 12.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
13. 13.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
14. 14.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
15. 15.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) 27 times (c) 6 times (d) 9 times
16. 16.A cuboid is 7 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 95 sq cm (b) 126 sq cm (c) 190 sq cm (d) 380 sq cm
17. 17.A cuboid is 8 cm long, 7 cm wide and 4 cm high. What is its total surface area? (a) 116 sq cm (b) 232 sq cm (c) 224 sq cm (d) 464 sq cm
18. 18.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
19. 19.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
20. 20.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 324 sq cm (c) 486 sq cm (d) 81 sq cm
21. 21.A cuboid is 9 cm long, 7 cm wide and 2 cm high. What is its volume? (a) 18 cu cm (b) 63 cu cm (c) 190 cu cm (d) 126 cu cm
22. 22.A cube has edges of 11 cm. What is its total surface area? (a) 726 sq cm (b) 121 sq cm (c) 1331 sq cm (d) 484 sq cm
23. 23.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
24. 24.A cube has edges of 11 cm. What is its volume? (a) 33 cu cm (b) 484 cu cm (c) 726 cu cm (d) 1331 cu cm
25. 25.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
26. 26.A cuboid is 4 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 80 sq cm (b) 40 sq cm (c) 48 sq cm (d) 160 sq cm
27. 27.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 440 cm (d) 110 cm
28. 28.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 4 times (c) 5 times (d) 2 times
29. 29.A cuboid is 9 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 252 cu cm (b) 254 cu cm (c) 20 cu cm (d) 36 cu cm
30. 30.A cuboid is 12 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 72 cu cm (b) 132 cu cm (c) 17 cu cm (d) 36 cu cm
31. 31.A cuboid is 4 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 36 sq cm (b) 33 sq cm (c) 66 sq cm (d) 132 sq cm
32. 32.A cuboid is 4 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 188 sq cm (b) 60 sq cm (c) 47 sq cm (d) 94 sq cm
33. 33.A cube has edges of 7 cm. What is its total surface area? (a) 343 sq cm (b) 196 sq cm (c) 294 sq cm (d) 49 sq cm
34. 34.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
35. 35.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 16 times (c) 8 times (d) 4 times
36. 36.A cuboid is 10 cm long, 8 cm wide and 8 cm high. What is its volume? (a) 80 cu cm (b) 448 cu cm (c) 640 cu cm (d) 26 cu cm
37. 37.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
38. 38.A cuboid is 10 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 69 sq cm (b) 276 sq cm (c) 90 sq cm (d) 138 sq cm
39. 39.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
40. 40.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 40 sq cm (b) 16 sq cm (c) 80 sq cm (d) 20 sq cm

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