Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 198 · 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 volume? (a) 54 cu cm (b) 36 cu cm (c) 27 cu cm (d) 9 cu cm
2. 2.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 1386 cm (d) 66 cm
3. 3.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
4. 4.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
5. 5.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
6. 6.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 12 cu cm (b) 7 cu cm (c) 6 cu cm (d) 32 cu cm
7. 7.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 729 cu cm (c) 486 cu cm (d) 27 cu cm
8. 8.A cuboid is 9 cm long, 6 cm wide and 2 cm high. What is its volume? (a) 54 cu cm (b) 17 cu cm (c) 168 cu cm (d) 108 cu cm
9. 9.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 176 sq cm
10. 10.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 96 sq cm (c) 64 sq cm (d) 97 sq cm
11. 11.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
12. 12.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 1386 sq cm
13. 13.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 4 times (d) 8 times
14. 14.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) 3 times (c) 9 times (d) 6 times
15. 15.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
16. 16.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 44 cm (d) 616 cm
17. 17.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 8 times (c) 6 times (d) 4 times
18. 18.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 3850 cm (d) 440 cm
19. 19.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
20. 20.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 110 cm (d) 3850 cm
21. 21.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
22. 22.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
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) 5 times (b) 8 times (c) 2 times (d) 4 times
24. 24.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 125 times (c) 5 times (d) 25 times
25. 25.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 125 times (c) 25 times (d) 5 times
26. 26.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 352 cm (d) 88 cm
27. 27.A cuboid is 4 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 104 sq cm (b) 52 sq cm (c) 24 sq cm (d) 26 sq cm
28. 28.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) 8 times (c) 16 times (d) 64 times
29. 29.A cuboid is 6 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 90 sq cm (b) 126 sq cm (c) 63 sq cm (d) 252 sq cm
30. 30.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
31. 31.A cuboid is 6 cm long, 4 cm wide and 9 cm high. What is its volume? (a) 24 cu cm (b) 216 cu cm (c) 228 cu cm (d) 19 cu cm
32. 32.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
33. 33.A cuboid is 8 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 216 cu cm (b) 24 cu cm (c) 20 cu cm (d) 246 cu cm
34. 34.A cuboid is 10 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 20 cu cm (b) 184 cu cm (c) 18 cu cm (d) 120 cu cm
35. 35.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 256 cu cm (c) 384 cu cm (d) 24 cu cm
36. 36.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 16 times (c) 8 times (d) 4 times
37. 37.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
38. 38.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq cm
39. 39.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
40. 40.A cube has edges of 8 cm. What is its total surface area? (a) 384 sq cm (b) 256 sq cm (c) 512 sq cm (d) 64 sq cm

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