Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 547 · 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.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
2. 2.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) 3 times (c) 27 times (d) 6 times
3. 3.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
4. 4.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
5. 5.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) 4 times (c) 2 times (d) 8 times
6. 6.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
7. 7.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) 25 times (c) 5 times (d) 125 times
8. 8.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 100 cu cm (c) 125 cu cm (d) 15 cu cm
9. 9.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) 27 times (c) 9 times (d) 3 times
10. 10.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
11. 11.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
12. 12.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
13. 13.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
14. 14.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
15. 15.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
16. 16.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 16 times (c) 64 times (d) 4 times
17. 17.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
18. 18.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 2 times (c) 8 times (d) 5 times
19. 19.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
20. 20.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 616 sq cm
21. 21.If the side of a square 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
22. 22.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 27 cu cm (c) 54 cu cm (d) 9 cu cm
23. 23.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 64 cu cm (c) 65 cu cm (d) 12 cu cm
24. 24.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm
25. 25.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 1000 cu cm (c) 400 cu cm (d) 30 cu cm
26. 26.A cuboid is 8 cm long, 4 cm wide and 4 cm high. What is its total surface area? (a) 128 sq cm (b) 160 sq cm (c) 80 sq cm (d) 320 sq cm
27. 27.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
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) 10 times (b) 125 times (c) 25 times (d) 5 times
29. 29.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) 6 times (c) 3 times (d) 9 times
30. 30.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
31. 31.A cuboid is 10 cm long, 9 cm wide and 8 cm high. What is its volume? (a) 27 cu cm (b) 720 cu cm (c) 484 cu cm (d) 90 cu cm
32. 32.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 729 sq cm (c) 81 sq cm (d) 486 sq cm
33. 33.A cube has edges of 4 cm. What is its total surface area? (a) 96 sq cm (b) 97 sq cm (c) 64 sq cm (d) 16 sq cm
34. 34.A cuboid is 7 cm long, 5 cm wide and 3 cm high. What is its volume? (a) 142 cu cm (b) 105 cu cm (c) 35 cu cm (d) 15 cu cm
35. 35.A cuboid is 12 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 656 sq cm (b) 240 sq cm (c) 328 sq cm (d) 164 sq cm
36. 36.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) 4 times (c) 8 times (d) 6 times
37. 37.A cuboid is 4 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 66 cu cm (b) 36 cu cm (c) 12 cu cm (d) 10 cu cm
38. 38.A cuboid is 8 cm long, 5 cm wide and 7 cm high. What is its total surface area? (a) 524 sq cm (b) 262 sq cm (c) 280 sq cm (d) 131 sq cm
39. 39.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 32 sq cm (b) 65 sq cm (c) 128 sq cm (d) 64 sq cm
40. 40.A cuboid is 4 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 300 sq cm (b) 108 sq cm (c) 150 sq cm (d) 75 sq cm

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