Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 655 · 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 3 times as long, how many times as big does its area become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
2. 2.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 44 sq cm (d) 616 sq cm
3. 3.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
4. 4.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
5. 5.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
6. 6.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
7. 7.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) 8 times (c) 4 times (d) 16 times
8. 8.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 132 cm (d) 264 cm
9. 9.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
10. 10.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 18 cu cm (b) 8 cu cm (c) 42 cu cm (d) 6 cu cm
11. 11.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 10 times (c) 5 times (d) 125 times
12. 12.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 4 times (c) 2 times (d) 8 times
13. 13.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 616 cm (d) 176 cm
14. 14.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) 9 times (c) 6 times (d) 27 times
15. 15.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 88 sq cm
16. 16.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 25 times (b) 10 times (c) 125 times (d) 5 times
17. 17.A cube has edges of 11 cm. What is its volume? (a) 33 cu cm (b) 726 cu cm (c) 484 cu cm (d) 1331 cu cm
18. 18.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
19. 19.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
20. 20.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) 64 times (c) 8 times (d) 16 times
21. 21.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 110 cm (d) 440 cm
22. 22.A cuboid is 12 cm long, 4 cm wide and 5 cm high. What is its total surface area? (a) 512 sq cm (b) 256 sq cm (c) 240 sq cm (d) 128 sq cm
23. 23.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
24. 24.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 24 sq cm (c) 16 sq cm (d) 4 sq cm
25. 25.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 132 sq cm
26. 26.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 196 cu cm (c) 343 cu cm (d) 294 cu cm
27. 27.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
28. 28.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 16 cu cm (c) 6 cu cm (d) 8 cu cm
29. 29.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
30. 30.A cube has edges of 10 cm. What is its total surface area? (a) 1000 sq cm (b) 400 sq cm (c) 100 sq cm (d) 600 sq cm
31. 31.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) 4 times (c) 64 times (d) 16 times
32. 32.A cuboid is 12 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 240 sq cm (b) 164 sq cm (c) 656 sq cm (d) 328 sq cm
33. 33.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 128 sq cm (b) 65 sq cm (c) 64 sq cm (d) 32 sq cm
34. 34.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 125 sq cm (c) 150 sq cm (d) 25 sq cm
35. 35.A cube has edges of 6 cm. What is its total surface area? (a) 217 sq cm (b) 144 sq cm (c) 36 sq cm (d) 216 sq cm
36. 36.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
37. 37.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
38. 38.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
39. 39.A cuboid is 11 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 44 cu cm (b) 298 cu cm (c) 308 cu cm (d) 22 cu cm
40. 40.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm

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