Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 599 · 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 cuboid is 12 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 144 cu cm (b) 19 cu cm (c) 192 cu cm (d) 48 cu cm
2. 2.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
3. 3.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
4. 4.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 2464 cm (d) 88 cm
5. 5.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
6. 6.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 176 sq cm
7. 7.A cuboid is 5 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 66 sq cm (b) 132 sq cm (c) 80 sq cm (d) 264 sq cm
8. 8.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 352 cm (d) 88 cm
9. 9.A cuboid is 5 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 13 cu cm (b) 10 cu cm (c) 60 cu cm (d) 104 cu cm
10. 10.A cuboid is 6 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 18 cu cm (b) 184 cu cm (c) 12 cu cm (d) 120 cu cm
11. 11.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
12. 12.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
13. 13.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 6 cu cm (b) 112 cu cm (c) 60 cu cm (d) 15 cu cm
14. 14.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
15. 15.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 1232 sq cm
16. 16.A cuboid is 5 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 10 cu cm (b) 9 cu cm (c) 20 cu cm (d) 48 cu cm
17. 17.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
18. 18.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) 10 times (c) 25 times (d) 125 times
19. 19.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 4 times (c) 8 times (d) 16 times
20. 20.A cuboid is 4 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 40 sq cm (b) 152 sq cm (c) 38 sq cm (d) 76 sq cm
21. 21.A cuboid is 12 cm long, 4 cm wide and 4 cm high. What is its volume? (a) 20 cu cm (b) 192 cu cm (c) 224 cu cm (d) 48 cu cm
22. 22.A cuboid is 12 cm long, 9 cm wide and 9 cm high. What is its volume? (a) 594 cu cm (b) 972 cu cm (c) 30 cu cm (d) 108 cu cm
23. 23.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) 4 times (c) 2 times (d) 5 times
24. 24.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) 25 times (c) 10 times (d) 5 times
25. 25.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 64 cu cm (c) 12 cu cm (d) 65 cu cm
26. 26.A cuboid is 7 cm long, 6 cm wide and 4 cm high. What is its total surface area? (a) 376 sq cm (b) 94 sq cm (c) 168 sq cm (d) 188 sq cm
27. 27.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 8 times (c) 6 times (d) 2 times
28. 28.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
29. 29.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 184 sq cm (b) 92 sq cm (c) 46 sq cm (d) 48 sq cm
30. 30.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) 4 times (c) 5 times (d) 2 times
31. 31.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
32. 32.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
33. 33.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
34. 34.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) 27 times (c) 6 times (d) 9 times
35. 35.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) 9 times (d) 27 times
36. 36.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 36 cu cm (c) 1728 cu cm (d) 576 cu cm
37. 37.A cuboid is 10 cm long, 4 cm wide and 8 cm high. What is its total surface area? (a) 608 sq cm (b) 304 sq cm (c) 320 sq cm (d) 152 sq cm
38. 38.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
39. 39.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 25 times (d) 10 times
40. 40.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 256 cu cm (c) 24 cu cm (d) 384 cu cm

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