Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 771 · 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.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 486 cu cm (c) 324 cu cm (d) 729 cu cm
2. 2.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
3. 3.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
4. 4.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
5. 5.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
6. 6.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 1331 cu cm (c) 726 cu cm (d) 33 cu cm
7. 7.A cube has edges of 6 cm. What is its volume? (a) 216 cu cm (b) 144 cu cm (c) 217 cu cm (d) 18 cu cm
8. 8.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
9. 9.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
10. 10.A cuboid is 9 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 212 cu cm (b) 18 cu cm (c) 19 cu cm (d) 144 cu cm
11. 11.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 88 cm (d) 352 cm
12. 12.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 sq cm
13. 13.A cuboid is 6 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 12 cu cm (b) 90 cu cm (c) 18 cu cm (d) 54 cu cm
14. 14.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
15. 15.A cube has edges of 5 cm. What is its total surface area? (a) 150 sq cm (b) 25 sq cm (c) 100 sq cm (d) 125 sq cm
16. 16.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
17. 17.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
18. 18.A cuboid is 5 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 70 cu cm (b) 10 cu cm (c) 14 cu cm (d) 118 cu cm
19. 19.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
20. 20.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
21. 21.If the side of a square 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
22. 22.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 97 sq cm (c) 16 sq cm (d) 96 sq cm
23. 23.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 8 cu cm (c) 6 cu cm (d) 24 cu cm
24. 24.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 3 times (c) 27 times (d) 6 times
25. 25.A cuboid is 11 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 110 sq cm (b) 348 sq cm (c) 87 sq cm (d) 174 sq cm
26. 26.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 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) 4 times (b) 16 times (c) 8 times (d) 64 times
28. 28.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 9 times (c) 3 times (d) 27 times
29. 29.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 125 times (c) 25 times (d) 10 times
30. 30.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 729 sq cm (c) 81 sq cm (d) 486 sq cm
31. 31.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
32. 32.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 112 sq cm (b) 60 sq cm (c) 224 sq cm (d) 56 sq cm
33. 33.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) 16 times (c) 64 times (d) 4 times
34. 34.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) 6 times (c) 27 times (d) 3 times
35. 35.A cuboid is 6 cm long, 5 cm wide and 9 cm high. What is its total surface area? (a) 516 sq cm (b) 270 sq cm (c) 258 sq cm (d) 129 sq cm
36. 36.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) 8 times (c) 4 times (d) 5 times
37. 37.A cuboid is 10 cm long, 7 cm wide and 6 cm high. What is its total surface area? (a) 688 sq cm (b) 344 sq cm (c) 420 sq cm (d) 172 sq cm
38. 38.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
39. 39.A cuboid is 5 cm long, 4 cm wide and 6 cm high. What is its volume? (a) 120 cu cm (b) 15 cu cm (c) 20 cu cm (d) 148 cu cm
40. 40.A cuboid is 4 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 12 cu cm (b) 10 cu cm (c) 36 cu cm (d) 66 cu cm

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