Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 464 · 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 5 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 12 cu cm (b) 60 cu cm (c) 94 cu cm (d) 20 cu cm
2. 2.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
3. 3.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) 27 times (c) 3 times (d) 9 times
4. 4.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
5. 5.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 10 times (c) 5 times (d) 125 times
6. 6.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 77 sq cm (d) 616 sq cm
7. 7.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 343 cu cm (c) 196 cu cm (d) 21 cu cm
8. 8.A cuboid is 11 cm long, 8 cm wide and 6 cm high. What is its total surface area? (a) 404 sq cm (b) 808 sq cm (c) 528 sq cm (d) 202 sq cm
9. 9.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
10. 10.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 176 sq cm
11. 11.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 6 cu cm (c) 24 cu cm (d) 16 cu cm
12. 12.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
13. 13.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 25 times (c) 10 times (d) 5 times
14. 14.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
15. 15.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 36 cu cm (c) 1728 cu cm (d) 864 cu cm
16. 16.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 726 sq cm (c) 484 sq cm (d) 121 sq cm
17. 17.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 3 times (c) 6 times (d) 27 times
18. 18.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 9 times (c) 3 times (d) 27 times
19. 19.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
20. 20.A cuboid is 11 cm long, 4 cm wide and 5 cm high. What is its volume? (a) 44 cu cm (b) 238 cu cm (c) 220 cu cm (d) 20 cu cm
21. 21.A cube has edges of 10 cm. What is its total surface area? (a) 1000 sq cm (b) 400 sq cm (c) 600 sq cm (d) 100 sq cm
22. 22.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 9856 sq cm
23. 23.A cube has edges of 11 cm. What is its volume? (a) 1331 cu cm (b) 33 cu cm (c) 484 cu cm (d) 726 cu cm
24. 24.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm
25. 25.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 100 cu cm (c) 125 cu cm (d) 150 cu cm
26. 26.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 24 sq cm (c) 8 sq cm (d) 4 sq cm
27. 27.A cuboid is 8 cm long, 4 cm wide and 7 cm high. What is its total surface area? (a) 224 sq cm (b) 116 sq cm (c) 232 sq cm (d) 464 sq cm
28. 28.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 5 times (c) 25 times (d) 10 times
29. 29.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) 2 times (c) 5 times (d) 4 times
30. 30.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
31. 31.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
32. 32.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) 8 times (c) 64 times (d) 4 times
33. 33.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 616 cm (d) 176 cm
34. 34.A cuboid is 12 cm long, 9 cm wide and 2 cm high. What is its volume? (a) 216 cu cm (b) 23 cu cm (c) 300 cu cm (d) 108 cu cm
35. 35.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 2 times (c) 5 times (d) 8 times
36. 36.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 97 sq cm (c) 96 sq cm (d) 64 sq cm
37. 37.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
38. 38.A cuboid is 10 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 400 cu cm (b) 360 cu cm (c) 40 cu cm (d) 24 cu cm
39. 39.A cuboid is 6 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 24 cu cm (b) 13 cu cm (c) 108 cu cm (d) 72 cu cm
40. 40.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) 125 times (c) 10 times (d) 5 times

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