Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 846 · 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 radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
2. 2.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
3. 3.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 616 sq cm (d) 44 sq cm
4. 4.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
5. 5.A cuboid is 10 cm long, 5 cm wide and 3 cm high. What is its total surface area? (a) 190 sq cm (b) 150 sq cm (c) 95 sq cm (d) 380 sq cm
6. 6.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 693 sq cm (d) 5544 sq cm
7. 7.A cuboid is 7 cm long, 6 cm wide and 7 cm high. What is its volume? (a) 20 cu cm (b) 42 cu cm (c) 294 cu cm (d) 266 cu cm
8. 8.A cuboid is 10 cm long, 8 cm wide and 3 cm high. What is its total surface area? (a) 240 sq cm (b) 536 sq cm (c) 134 sq cm (d) 268 sq cm
9. 9.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
10. 10.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
11. 11.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
12. 12.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
13. 13.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 9 sq cm (c) 27 sq cm (d) 54 sq cm
14. 14.A cube has edges of 11 cm. What is its total surface area? (a) 484 sq cm (b) 121 sq cm (c) 726 sq cm (d) 1331 sq cm
15. 15.A cuboid is 4 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 15 cu cm (b) 8 cu cm (c) 72 cu cm (d) 124 cu cm
16. 16.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 294 sq cm (c) 49 sq cm (d) 343 sq cm
17. 17.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 6 cu cm (b) 13 cu cm (c) 48 cu cm (d) 92 cu cm
18. 18.A cuboid is 4 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 150 cu cm (b) 108 cu cm (c) 12 cu cm (d) 16 cu cm
19. 19.A cube has edges of 9 cm. What is its total surface area? (a) 486 sq cm (b) 324 sq cm (c) 729 sq cm (d) 81 sq cm
20. 20.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) 5 times (c) 10 times (d) 125 times
21. 21.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
22. 22.A cuboid is 5 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 174 cu cm (b) 135 cu cm (c) 15 cu cm (d) 17 cu cm
23. 23.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
24. 24.A cuboid is 6 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 126 cu cm (b) 162 cu cm (c) 18 cu cm (d) 16 cu cm
25. 25.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 196 cu cm (c) 294 cu cm (d) 343 cu cm
26. 26.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
27. 27.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 16 times (c) 64 times (d) 4 times
28. 28.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 24 cu cm (c) 256 cu cm (d) 512 cu cm
29. 29.A cube has edges of 11 cm. What is its volume? (a) 33 cu cm (b) 484 cu cm (c) 1331 cu cm (d) 726 cu cm
30. 30.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
31. 31.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 110 cm (d) 220 cm
32. 32.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 64 times (c) 16 times (d) 4 times
33. 33.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 64 times (d) 16 times
34. 34.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 864 cu cm (c) 1728 cu cm (d) 36 cu cm
35. 35.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) 5 times (c) 2 times (d) 4 times
36. 36.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
37. 37.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
38. 38.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 125 times (c) 25 times (d) 10 times
39. 39.A cube has edges of 8 cm. What is its total surface area? (a) 256 sq cm (b) 512 sq cm (c) 384 sq cm (d) 64 sq cm
40. 40.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) 9 times (c) 6 times (d) 27 times

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