Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 70 · 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) 616 cm (b) 88 cm (c) 176 cm (d) 44 cm
2. 2.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 132 sq cm (d) 5544 sq cm
3. 3.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
4. 4.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm
5. 5.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 10 cu cm (b) 62 cu cm (c) 6 cu cm (d) 30 cu cm
6. 6.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) 25 times (c) 10 times (d) 5 times
7. 7.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) 5 times (c) 8 times (d) 2 times
8. 8.A cube has edges of 12 cm. What is its total surface area? (a) 1728 sq cm (b) 144 sq cm (c) 864 sq cm (d) 576 sq cm
9. 9.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 512 sq cm (c) 256 sq cm (d) 384 sq cm
10. 10.A cuboid is 7 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 28 cu cm (b) 18 cu cm (c) 196 cu cm (d) 210 cu cm
11. 11.A cube has edges of 9 cm. What is its volume? (a) 729 cu cm (b) 486 cu cm (c) 27 cu cm (d) 324 cu cm
12. 12.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
13. 13.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 44 sq cm (d) 616 sq cm
14. 14.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 9856 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) 25 times (c) 5 times (d) 125 times
16. 16.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
17. 17.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 8 times (c) 4 times (d) 64 times
18. 18.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 3 times (c) 6 times (d) 9 times
19. 19.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
20. 20.A cuboid is 9 cm long, 7 cm wide and 4 cm high. What is its volume? (a) 252 cu cm (b) 63 cu cm (c) 254 cu cm (d) 20 cu cm
21. 21.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 12 sq cm (b) 64 sq cm (c) 16 sq cm (d) 32 sq cm
22. 22.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
23. 23.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 121 sq cm (c) 726 sq cm (d) 484 sq cm
24. 24.A cuboid is 7 cm long, 6 cm wide and 9 cm high. What is its volume? (a) 318 cu cm (b) 42 cu cm (c) 22 cu cm (d) 378 cu cm
25. 25.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 80 sq cm (b) 16 sq cm (c) 40 sq cm (d) 20 sq cm
26. 26.A cube has edges of 6 cm. What is its volume? (a) 144 cu cm (b) 217 cu cm (c) 216 cu cm (d) 18 cu cm
27. 27.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
28. 28.A cuboid is 5 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 38 sq cm (b) 40 sq cm (c) 76 sq cm (d) 152 sq cm
29. 29.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
30. 30.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq cm
31. 31.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
32. 32.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 110 cm (d) 440 cm
33. 33.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 21 cu cm (c) 294 cu cm (d) 343 cu cm
34. 34.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
35. 35.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 2464 cm (d) 88 cm
36. 36.A cuboid is 6 cm long, 5 cm wide and 6 cm high. What is its volume? (a) 192 cu cm (b) 30 cu cm (c) 180 cu cm (d) 17 cu cm
37. 37.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) 6 times (c) 27 times (d) 9 times
38. 38.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 100 cu cm (c) 150 cu cm (d) 125 cu cm
39. 39.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 5 times (c) 125 times (d) 25 times
40. 40.A cuboid is 11 cm long, 6 cm wide and 3 cm high. What is its volume? (a) 234 cu cm (b) 198 cu cm (c) 66 cu cm (d) 20 cu cm

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