Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 679 · 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.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times
2. 2.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
3. 3.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
4. 4.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 6 times (c) 3 times (d) 27 times
5. 5.A cube has edges of 11 cm. What is its volume? (a) 726 cu cm (b) 33 cu cm (c) 484 cu cm (d) 1331 cu cm
6. 6.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
7. 7.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 44 cm (d) 176 cm
8. 8.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) 4 times (d) 2 times
9. 9.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 1386 cm (d) 264 cm
10. 10.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 16 times (c) 64 times (d) 8 times
11. 11.A cuboid is 11 cm long, 6 cm wide and 5 cm high. What is its volume? (a) 330 cu cm (b) 22 cu cm (c) 66 cu cm (d) 302 cu cm
12. 12.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
13. 13.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
14. 14.A cuboid is 6 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 73 sq cm (b) 72 sq cm (c) 144 sq cm (d) 36 sq cm
15. 15.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 16 cu cm (c) 6 cu cm (d) 24 cu cm
16. 16.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
17. 17.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) 5 times (d) 2 times
18. 18.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
19. 19.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
20. 20.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
21. 21.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 44 sq cm (d) 154 sq cm
22. 22.A cuboid is 12 cm long, 5 cm wide and 2 cm high. What is its total surface area? (a) 188 sq cm (b) 120 sq cm (c) 94 sq cm (d) 376 sq cm
23. 23.A cuboid is 12 cm long, 6 cm wide and 4 cm high. What is its volume? (a) 72 cu cm (b) 289 cu cm (c) 288 cu cm (d) 22 cu cm
24. 24.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
25. 25.A cuboid is 12 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 300 cu cm (b) 24 cu cm (c) 23 cu cm (d) 216 cu cm
26. 26.A cuboid is 6 cm long, 5 cm wide and 10 cm high. What is its volume? (a) 30 cu cm (b) 21 cu cm (c) 300 cu cm (d) 280 cu cm
27. 27.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 352 cm (d) 176 cm
28. 28.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
29. 29.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
30. 30.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 9 times (c) 6 times (d) 3 times
31. 31.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 9856 sq cm
32. 32.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
33. 33.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 27 sq cm (c) 9 sq cm (d) 54 sq cm
34. 34.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) 8 times (c) 64 times (d) 16 times
35. 35.A cuboid is 8 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 17 cu cm (b) 24 cu cm (c) 180 cu cm (d) 144 cu 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) 4 times (b) 8 times (c) 2 times (d) 5 times
37. 37.A cuboid is 10 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 464 sq cm (b) 232 sq cm (c) 160 sq cm (d) 116 sq cm
38. 38.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) 9 times (c) 3 times (d) 27 times
39. 39.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 100 cu cm (c) 15 cu cm (d) 125 cu cm
40. 40.A cuboid is 4 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 56 sq cm (b) 224 sq cm (c) 112 sq cm (d) 64 sq cm

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