Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 498 · 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.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 9 times (c) 6 times (d) 27 times
2. 2.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 12 cu cm (b) 42 cu cm (c) 82 cu cm (d) 6 cu cm
3. 3.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
4. 4.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
5. 5.A cuboid is 6 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 188 cu cm (b) 24 cu cm (c) 17 cu cm (d) 168 cu cm
6. 6.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
7. 7.If the side of a square 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
8. 8.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
9. 9.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
10. 10.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
11. 11.A cuboid is 9 cm long, 6 cm wide and 3 cm high. What is its volume? (a) 18 cu cm (b) 162 cu cm (c) 54 cu cm (d) 198 cu cm
12. 12.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
13. 13.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
14. 14.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
15. 15.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 125 cu cm (c) 100 cu cm (d) 15 cu cm
16. 16.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 1232 sq cm
17. 17.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 176 sq cm
18. 18.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
19. 19.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
20. 20.A cuboid is 12 cm long, 8 cm wide and 10 cm high. What is its volume? (a) 30 cu cm (b) 592 cu cm (c) 96 cu cm (d) 960 cu cm
21. 21.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq cm
22. 22.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 104 sq cm (b) 26 sq cm (c) 52 sq cm (d) 24 sq cm
23. 23.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
24. 24.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
25. 25.A cube has edges of 3 cm. What is its total surface area? (a) 54 sq cm (b) 9 sq cm (c) 27 sq cm (d) 36 sq cm
26. 26.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 6 times (c) 3 times (d) 9 times
27. 27.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
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.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 6 cu cm (c) 24 cu cm (d) 8 cu cm
30. 30.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
31. 31.A cube has edges of 10 cm. What is its total surface area? (a) 100 sq cm (b) 1000 sq cm (c) 600 sq cm (d) 400 sq cm
32. 32.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
33. 33.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) 8 times (c) 4 times (d) 5 times
34. 34.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 77 sq cm (d) 616 sq cm
35. 35.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 6 times (c) 9 times (d) 27 times
36. 36.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 65 cu cm (c) 64 cu cm (d) 12 cu cm
37. 37.If the radius of a circle 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
38. 38.A cuboid is 5 cm long, 4 cm wide and 3 cm high. What is its total surface area? (a) 188 sq cm (b) 94 sq cm (c) 47 sq cm (d) 60 sq cm
39. 39.If the radius of a circle 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
40. 40.A cuboid is 5 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 94 cu cm (b) 20 cu cm (c) 12 cu cm (d) 60 cu cm

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