Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 845 · 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 every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 64 times (c) 16 times (d) 4 times
2. 2.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 600 cu cm (c) 400 cu cm (d) 30 cu cm
3. 3.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
4. 4.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 616 cm (d) 176 cm
5. 5.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
6. 6.A cuboid is 10 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 161 cu cm (b) 160 cu cm (c) 20 cu cm (d) 232 cu cm
7. 7.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
8. 8.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 96 sq cm (c) 64 sq cm (d) 16 sq cm
9. 9.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 49 sq cm (c) 343 sq cm (d) 294 sq cm
10. 10.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
11. 11.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
12. 12.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 9 sq cm (c) 36 sq cm (d) 54 sq cm
13. 13.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
14. 14.A cube has edges of 8 cm. What is its total surface area? (a) 384 sq cm (b) 64 sq cm (c) 512 sq cm (d) 256 sq cm
15. 15.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 sq cm
16. 16.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
17. 17.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
18. 18.A cuboid is 6 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 13 cu cm (b) 108 cu cm (c) 24 cu cm (d) 72 cu cm
19. 19.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
20. 20.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) 8 times (c) 5 times (d) 4 times
21. 21.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 27 cu cm (c) 54 cu cm (d) 9 cu cm
22. 22.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
23. 23.A cuboid is 4 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 40 sq cm (b) 76 sq cm (c) 38 sq cm (d) 152 sq cm
24. 24.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 1386 cm (d) 264 cm
25. 25.A cuboid is 7 cm long, 5 cm wide and 4 cm high. What is its total surface area? (a) 140 sq cm (b) 332 sq cm (c) 83 sq cm (d) 166 sq cm
26. 26.A cube has edges of 11 cm. What is its volume? (a) 1331 cu cm (b) 726 cu cm (c) 484 cu cm (d) 33 cu cm
27. 27.A cuboid is 10 cm long, 6 cm wide and 5 cm high. What is its total surface area? (a) 300 sq cm (b) 280 sq cm (c) 560 sq cm (d) 140 sq cm
28. 28.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
29. 29.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
30. 30.A cube has edges of 4 cm. What is its volume? (a) 64 cu cm (b) 65 cu cm (c) 12 cu cm (d) 96 cu cm
31. 31.A cuboid is 5 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 20 cu cm (b) 94 cu cm (c) 12 cu cm (d) 60 cu cm
32. 32.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 196 cu cm (c) 343 cu cm (d) 21 cu cm
33. 33.A cuboid is 12 cm long, 11 cm wide and 5 cm high. What is its volume? (a) 28 cu cm (b) 660 cu cm (c) 132 cu cm (d) 494 cu cm
34. 34.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) 10 times (c) 25 times (d) 5 times
35. 35.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
36. 36.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 2 times (c) 4 times (d) 6 times
37. 37.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
38. 38.A cuboid is 4 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 33 sq cm (b) 36 sq cm (c) 132 sq cm (d) 66 sq cm
39. 39.If the radius of a circle 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
40. 40.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 125 cu cm (c) 150 cu cm (d) 100 cu cm

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