Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 827 · 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 3 cm. What is its total surface area? (a) 9 sq cm (b) 54 sq cm (c) 27 sq cm (d) 36 sq cm
2. 2.A cube has edges of 10 cm. What is its volume? (a) 400 cu cm (b) 1000 cu cm (c) 30 cu cm (d) 600 cu cm
3. 3.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 77 sq cm (d) 616 sq cm
4. 4.A cuboid is 10 cm long, 6 cm wide and 5 cm high. What is its volume? (a) 60 cu cm (b) 300 cu cm (c) 21 cu cm (d) 280 cu cm
5. 5.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
6. 6.A cube has edges of 11 cm. What is its total surface area? (a) 121 sq cm (b) 484 sq cm (c) 726 sq cm (d) 1331 sq cm
7. 7.A cube has edges of 6 cm. What is its total surface area? (a) 217 sq cm (b) 36 sq cm (c) 216 sq cm (d) 144 sq cm
8. 8.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm
9. 9.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
10. 10.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) 25 times (c) 10 times (d) 5 times
11. 11.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 693 sq cm (d) 5544 sq cm
12. 12.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 88 sq cm
13. 13.A cuboid is 9 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 108 cu cm (b) 16 cu cm (c) 36 cu cm (d) 150 cu cm
14. 14.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
15. 15.A cuboid is 9 cm long, 4 cm wide and 3 cm high. What is its total surface area? (a) 75 sq cm (b) 108 sq cm (c) 300 sq cm (d) 150 sq cm
16. 16.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 616 sq cm (d) 88 sq cm
17. 17.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 1232 sq cm
18. 18.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
19. 19.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 15 cu cm (c) 100 cu cm (d) 125 cu cm
20. 20.A cube has edges of 8 cm. What is its total surface area? (a) 256 sq cm (b) 64 sq cm (c) 512 sq cm (d) 384 sq cm
21. 21.A cuboid is 10 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 184 sq cm (b) 368 sq cm (c) 120 sq cm (d) 92 sq cm
22. 22.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
23. 23.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 16 times (c) 64 times (d) 4 times
24. 24.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
25. 25.A cuboid is 8 cm long, 6 cm wide and 7 cm high. What is its volume? (a) 48 cu cm (b) 336 cu cm (c) 21 cu cm (d) 292 cu cm
26. 26.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 5 times (c) 8 times (d) 4 times
27. 27.A cuboid is 7 cm long, 5 cm wide and 7 cm high. What is its volume? (a) 245 cu cm (b) 238 cu cm (c) 35 cu cm (d) 19 cu cm
28. 28.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 9 times (c) 3 times (d) 6 times
29. 29.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 2464 cm (d) 352 cm
30. 30.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 54 cu cm (c) 27 cu cm (d) 36 cu cm
31. 31.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
32. 32.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
33. 33.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 10 times (c) 5 times (d) 25 times
34. 34.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) 10 times (c) 5 times (d) 25 times
35. 35.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
36. 36.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 12 cu cm (c) 65 cu cm (d) 64 cu cm
37. 37.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 27 times (c) 6 times (d) 3 times
38. 38.A cube has edges of 10 cm. What is its total surface area? (a) 1000 sq cm (b) 100 sq cm (c) 600 sq cm (d) 400 sq cm
39. 39.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
40. 40.A cuboid is 7 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 142 cu cm (b) 15 cu cm (c) 21 cu cm (d) 105 cu cm

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