Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 695 · 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 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 2464 cm (d) 352 cm
2. 2.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 24 cu cm (c) 6 cu cm (d) 8 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) 8 times (c) 4 times (d) 2 times
4. 4.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
5. 5.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
6. 6.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) 5 times (d) 4 times
7. 7.A cuboid is 11 cm long, 6 cm wide and 10 cm high. What is its volume? (a) 66 cu cm (b) 27 cu cm (c) 472 cu cm (d) 660 cu cm
8. 8.A cube has edges of 7 cm. What is its total surface area? (a) 294 sq cm (b) 196 sq cm (c) 49 sq cm (d) 343 sq cm
9. 9.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 8 sq cm (c) 4 sq cm (d) 24 sq cm
10. 10.A cuboid is 5 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 52 sq cm (b) 208 sq cm (c) 104 sq cm (d) 60 sq cm
11. 11.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 66 cm (d) 1386 cm
12. 12.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 616 sq cm
13. 13.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 1232 sq cm
14. 14.A cuboid is 4 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 48 sq cm (b) 176 sq cm (c) 44 sq cm (d) 88 sq cm
15. 15.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) 5 times (c) 125 times (d) 25 times
16. 16.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
17. 17.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 176 cm (d) 616 cm
18. 18.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 576 cu cm (c) 36 cu cm (d) 1728 cu cm
19. 19.A cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 100 sq cm (c) 400 sq cm (d) 1000 sq cm
20. 20.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
21. 21.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 3850 cm (d) 440 cm
22. 22.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
23. 23.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 15 cu cm (c) 100 cu cm (d) 150 cu cm
24. 24.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 486 sq cm (c) 729 sq cm (d) 324 sq cm
25. 25.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
26. 26.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 30 cu cm (c) 400 cu cm (d) 1000 cu cm
27. 27.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
28. 28.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
29. 29.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 150 sq cm (c) 125 sq cm (d) 100 sq cm
30. 30.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 726 cu cm (c) 33 cu cm (d) 1331 cu cm
31. 31.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
32. 32.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
33. 33.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
34. 34.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
35. 35.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 729 cu cm (c) 324 cu cm (d) 486 cu cm
36. 36.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 384 sq cm (c) 256 sq cm (d) 64 sq cm
37. 37.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
38. 38.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) 27 times (c) 9 times (d) 6 times
39. 39.A cuboid is 4 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 112 sq cm (b) 64 sq cm (c) 56 sq cm (d) 224 sq cm
40. 40.A cuboid is 9 cm long, 5 cm wide and 4 cm high. What is its volume? (a) 45 cu cm (b) 18 cu cm (c) 202 cu cm (d) 180 cu cm

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