Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 761 · 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 area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
2. 2.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 4 times (c) 8 times (d) 2 times
3. 3.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
4. 4.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
5. 5.A cuboid is 4 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 100 cu cm (b) 8 cu cm (c) 13 cu cm (d) 56 cu cm
6. 6.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 132 cm (d) 264 cm
7. 7.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
8. 8.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) 16 times (c) 8 times (d) 64 times
9. 9.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times
10. 10.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm
11. 11.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) 5 times (c) 4 times (d) 8 times
12. 12.A cuboid is 11 cm long, 4 cm wide and 6 cm high. What is its volume? (a) 264 cu cm (b) 44 cu cm (c) 21 cu cm (d) 268 cu cm
13. 13.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 9 cu cm (c) 36 cu cm (d) 27 cu cm
14. 14.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 8 cu cm (c) 16 cu cm (d) 6 cu cm
15. 15.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 176 cm (d) 88 cm
16. 16.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
17. 17.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
18. 18.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 16 cu cm (b) 8 cu cm (c) 17 cu cm (d) 40 cu cm
19. 19.A cuboid is 12 cm long, 10 cm wide and 2 cm high. What is its volume? (a) 240 cu cm (b) 24 cu cm (c) 328 cu cm (d) 120 cu cm
20. 20.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
21. 21.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 726 cu cm (c) 1331 cu cm (d) 33 cu cm
22. 22.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 616 sq cm (d) 77 sq cm
23. 23.A cuboid is 7 cm long, 4 cm wide and 8 cm high. What is its volume? (a) 232 cu cm (b) 28 cu cm (c) 19 cu cm (d) 224 cu cm
24. 24.A cube has edges of 11 cm. What is its total surface area? (a) 484 sq cm (b) 121 sq cm (c) 1331 sq cm (d) 726 sq cm
25. 25.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm
26. 26.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
27. 27.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
28. 28.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 196 cu cm (c) 21 cu cm (d) 343 cu cm
29. 29.A cube has edges of 3 cm. What is its total surface area? (a) 54 sq cm (b) 27 sq cm (c) 9 sq cm (d) 36 sq cm
30. 30.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 125 times (b) 5 times (c) 10 times (d) 25 times
31. 31.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 92 cu cm (b) 6 cu cm (c) 13 cu cm (d) 48 cu cm
32. 32.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 216 cu cm (c) 144 cu cm (d) 18 cu cm
33. 33.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
34. 34.A cuboid is 6 cm long, 4 cm wide and 6 cm high. What is its total surface area? (a) 84 sq cm (b) 144 sq cm (c) 168 sq cm (d) 336 sq cm
35. 35.A cuboid is 12 cm long, 7 cm wide and 5 cm high. What is its volume? (a) 24 cu cm (b) 420 cu cm (c) 358 cu cm (d) 84 cu cm
36. 36.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 324 cu cm (c) 729 cu cm (d) 486 cu cm
37. 37.A cuboid is 5 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 132 cu cm (b) 80 cu cm (c) 15 cu cm (d) 10 cu cm
38. 38.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) 4 times (c) 2 times (d) 5 times
39. 39.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
40. 40.A cuboid is 10 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 138 cu cm (b) 16 cu cm (c) 30 cu cm (d) 90 cu cm

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