Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 898 · 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 4 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 8 cu cm (b) 72 cu cm (c) 15 cu cm (d) 124 cu cm
2. 2.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
3. 3.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 22 cm (d) 88 cm
4. 4.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
5. 5.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 150 sq cm (c) 125 sq cm (d) 25 sq cm
6. 6.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 88 cm (d) 352 cm
7. 7.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) 27 times (c) 6 times (d) 9 times
8. 8.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) 27 times (c) 6 times (d) 9 times
9. 9.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
10. 10.A cuboid is 5 cm long, 4 cm wide and 3 cm high. What is its total surface area? (a) 60 sq cm (b) 94 sq cm (c) 188 sq cm (d) 47 sq cm
11. 11.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 12 cu cm (c) 96 cu cm (d) 64 cu cm
12. 12.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
13. 13.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 176 sq cm
14. 14.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
15. 15.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 384 cu cm (c) 24 cu cm (d) 512 cu cm
16. 16.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
17. 17.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
18. 18.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
19. 19.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
20. 20.A cuboid is 5 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 31 cu cm (b) 10 cu cm (c) 62 cu cm (d) 30 cu cm
21. 21.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 132 cm (d) 264 cm
22. 22.A cube has edges of 7 cm. What is its total surface area? (a) 49 sq cm (b) 343 sq cm (c) 196 sq cm (d) 294 sq cm
23. 23.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
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) 10 times (c) 5 times (d) 25 times
25. 25.A cube has edges of 2 cm. What is its total surface area? (a) 24 sq cm (b) 16 sq cm (c) 4 sq cm (d) 8 sq cm
26. 26.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 4 times (c) 8 times (d) 64 times
27. 27.A cuboid is 11 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 88 cu cm (b) 148 cu cm (c) 44 cu cm (d) 17 cu cm
28. 28.A cube has edges of 10 cm. What is its total surface area? (a) 400 sq cm (b) 1000 sq cm (c) 600 sq cm (d) 100 sq cm
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) 10 times (c) 125 times (d) 25 times
30. 30.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 9 cu cm (c) 36 cu cm (d) 54 cu cm
31. 31.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
32. 32.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 16 sq cm (c) 97 sq cm (d) 96 sq cm
33. 33.A cuboid is 7 cm long, 5 cm wide and 10 cm high. What is its total surface area? (a) 310 sq cm (b) 350 sq cm (c) 155 sq cm (d) 620 sq cm
34. 34.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
35. 35.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 616 sq cm (d) 77 sq cm
36. 36.A cuboid is 8 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 132 cu cm (b) 15 cu cm (c) 80 cu cm (d) 16 cu cm
37. 37.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 2 times (c) 6 times (d) 4 times
38. 38.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 16 cu cm (c) 8 cu cm (d) 24 cu cm
39. 39.A cuboid is 10 cm long, 6 cm wide and 2 cm high. What is its volume? (a) 60 cu cm (b) 120 cu cm (c) 184 cu cm (d) 18 cu cm
40. 40.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm

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