Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 435 · 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.A cuboid is 11 cm long, 6 cm wide and 6 cm high. What is its volume? (a) 66 cu cm (b) 396 cu cm (c) 23 cu cm (d) 336 cu cm
2. 2.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 308 sq cm
3. 3.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 616 cm (d) 44 cm
4. 4.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 6 times (c) 27 times (d) 3 times
5. 5.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) 4 times (c) 8 times (d) 5 times
6. 6.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
7. 7.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 9856 sq cm
8. 8.A cuboid is 9 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 512 sq cm (b) 180 sq cm (c) 128 sq cm (d) 256 sq cm
9. 9.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
10. 10.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 3 times (c) 6 times (d) 27 times
11. 11.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
12. 12.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 110 cm (d) 440 cm
13. 13.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 80 sq cm (b) 20 sq cm (c) 40 sq cm (d) 16 sq cm
14. 14.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
15. 15.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 96 sq cm (c) 64 sq cm (d) 97 sq cm
16. 16.A cube has edges of 11 cm. What is its volume? (a) 33 cu cm (b) 1331 cu cm (c) 484 cu cm (d) 726 cu cm
17. 17.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 88 cm (d) 352 cm
18. 18.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 12 cu cm (c) 64 cu cm (d) 96 cu cm
19. 19.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) 5 times (c) 10 times (d) 125 times
20. 20.A cuboid is 10 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 160 sq cm (b) 300 sq cm (c) 640 sq cm (d) 320 sq cm
21. 21.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 616 sq cm
22. 22.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 400 cu cm (c) 1000 cu cm (d) 30 cu cm
23. 23.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 27 sq cm (c) 9 sq cm (d) 54 sq cm
24. 24.A cuboid is 4 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 76 sq cm (b) 38 sq cm (c) 152 sq cm (d) 40 sq cm
25. 25.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
26. 26.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 8 times (c) 2 times (d) 4 times
27. 27.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 10 times (c) 125 times (d) 5 times
28. 28.A cuboid is 8 cm long, 6 cm wide and 6 cm high. What is its total surface area? (a) 264 sq cm (b) 528 sq cm (c) 132 sq cm (d) 288 sq cm
29. 29.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 66 cm (d) 1386 cm
30. 30.A cube has edges of 2 cm. What is its total surface area? (a) 24 sq cm (b) 16 sq cm (c) 8 sq cm (d) 4 sq cm
31. 31.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
32. 32.A cuboid is 8 cm long, 7 cm wide and 2 cm high. What is its total surface area? (a) 112 sq cm (b) 172 sq cm (c) 344 sq cm (d) 86 sq cm
33. 33.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 64 times (c) 16 times (d) 4 times
34. 34.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
35. 35.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 3850 cm (d) 110 cm
36. 36.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 726 sq cm (c) 121 sq cm (d) 484 sq cm
37. 37.A cube has edges of 12 cm. What is its volume? (a) 1728 cu cm (b) 864 cu cm (c) 36 cu cm (d) 576 cu cm
38. 38.A cuboid is 9 cm long, 7 cm wide and 2 cm high. What is its total surface area? (a) 95 sq cm (b) 126 sq cm (c) 190 sq cm (d) 380 sq cm
39. 39.A cube has edges of 5 cm. What is its total surface area? (a) 150 sq cm (b) 100 sq cm (c) 125 sq cm (d) 25 sq cm
40. 40.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) 8 times (c) 2 times (d) 6 times

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