Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 434 · 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 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 352 cm (d) 176 cm
2. 2.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 24 cu cm (c) 512 cu cm (d) 256 cu cm
3. 3.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 308 sq cm
4. 4.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 9 times (c) 6 times (d) 3 times
5. 5.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) 5 times (c) 10 times (d) 125 times
6. 6.A cuboid is 5 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 48 sq cm (b) 96 sq cm (c) 20 sq cm (d) 24 sq cm
7. 7.A cuboid is 9 cm long, 4 cm wide and 5 cm high. What is its total surface area? (a) 180 sq cm (b) 404 sq cm (c) 202 sq cm (d) 101 sq cm
8. 8.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq 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) 27 times (b) 9 times (c) 6 times (d) 3 times
10. 10.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
11. 11.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
12. 12.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) 64 times (c) 8 times (d) 4 times
13. 13.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) 16 times (c) 64 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) 6 times (d) 9 times
15. 15.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
16. 16.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) 4 times (d) 6 times
17. 17.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
18. 18.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 1386 cm (d) 66 cm
19. 19.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
20. 20.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
21. 21.A cube has edges of 10 cm. What is its volume? (a) 30 cu cm (b) 600 cu cm (c) 400 cu cm (d) 1000 cu cm
22. 22.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) 8 times (c) 4 times (d) 2 times
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) 6 times (b) 27 times (c) 3 times (d) 9 times
24. 24.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 62 sq cm (b) 31 sq cm (c) 124 sq cm (d) 30 sq cm
25. 25.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 308 sq cm
26. 26.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 16 cu cm (c) 8 cu cm (d) 24 cu cm
27. 27.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
28. 28.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) 2 times (c) 8 times (d) 5 times
29. 29.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 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) 4 times (b) 8 times (c) 64 times (d) 16 times
31. 31.A cuboid is 10 cm long, 7 cm wide and 8 cm high. What is its total surface area? (a) 412 sq cm (b) 206 sq cm (c) 824 sq cm (d) 560 sq cm
32. 32.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
33. 33.A cuboid is 6 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 11 cu cm (b) 12 cu cm (c) 36 cu cm (d) 72 cu cm
34. 34.A cuboid is 7 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 14 cu cm (b) 11 cu cm (c) 64 cu cm (d) 28 cu cm
35. 35.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
36. 36.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 22 cm (d) 88 cm
37. 37.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
38. 38.A cuboid is 5 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 45 sq cm (b) 39 sq cm (c) 78 sq cm (d) 156 sq cm
39. 39.A cuboid is 11 cm long, 7 cm wide and 3 cm high. What is its volume? (a) 21 cu cm (b) 262 cu cm (c) 77 cu cm (d) 231 cu cm
40. 40.A cuboid is 7 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 82 cu cm (b) 14 cu cm (c) 42 cu cm (d) 12 cu cm

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