Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 383 · 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) 44 cm (c) 176 cm (d) 616 cm
2. 2.A cube has edges of 5 cm. What is its total surface area? (a) 125 sq cm (b) 25 sq cm (c) 150 sq cm (d) 100 sq cm
3. 3.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
4. 4.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 1728 sq cm (c) 144 sq cm (d) 576 sq cm
5. 5.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 729 sq cm (c) 486 sq cm (d) 324 sq cm
6. 6.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 440 cm (d) 220 cm
7. 7.A cuboid is 11 cm long, 9 cm wide and 2 cm high. What is its volume? (a) 99 cu cm (b) 22 cu cm (c) 278 cu cm (d) 198 cu cm
8. 8.A cube has edges of 10 cm. What is its total surface area? (a) 400 sq cm (b) 600 sq cm (c) 1000 sq cm (d) 100 sq cm
9. 9.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
10. 10.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) 16 times (c) 64 times (d) 4 times
11. 11.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) 8 times (c) 2 times (d) 5 times
12. 12.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 65 cu cm (c) 12 cu cm (d) 64 cu cm
13. 13.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 25 times (c) 10 times (d) 125 times
14. 14.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
15. 15.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 16 times (c) 8 times (d) 64 times
16. 16.A cuboid is 12 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 324 sq cm (b) 162 sq cm (c) 81 sq cm (d) 108 sq cm
17. 17.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 9856 sq cm
18. 18.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) 10 times (c) 25 times (d) 5 times
19. 19.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 100 cu cm (c) 15 cu cm (d) 125 cu cm
20. 20.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 88 cm (d) 154 cm
21. 21.A cube has edges of 12 cm. What is its volume? (a) 1728 cu cm (b) 576 cu cm (c) 864 cu cm (d) 36 cu cm
22. 22.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
23. 23.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) 3 times (c) 9 times (d) 6 times
24. 24.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 66 cm (d) 264 cm
25. 25.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 96 sq cm (c) 97 sq cm (d) 16 sq cm
26. 26.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
27. 27.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) 5 times (c) 8 times (d) 4 times
28. 28.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
29. 29.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 21 cu cm (c) 196 cu cm (d) 343 cu cm
30. 30.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
31. 31.A cuboid is 7 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 200 sq cm (b) 50 sq cm (c) 100 sq cm (d) 56 sq cm
32. 32.A cuboid is 4 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 9 cu cm (b) 52 cu cm (c) 8 cu cm (d) 24 cu cm
33. 33.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
34. 34.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) 27 times (d) 6 times
35. 35.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
36. 36.A cuboid is 4 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 12 cu cm (b) 108 cu cm (c) 13 cu cm (d) 72 cu cm
37. 37.A cuboid is 5 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 60 cu cm (b) 94 cu cm (c) 15 cu cm (d) 12 cu cm
38. 38.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
39. 39.A cuboid is 6 cm long, 4 cm wide and 4 cm high. What is its total surface area? (a) 128 sq cm (b) 64 sq cm (c) 256 sq cm (d) 96 sq cm
40. 40.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm

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