Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 276 · 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 area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
2. 2.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 110 cm (d) 220 cm
3. 3.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
4. 4.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 352 cm (d) 2464 cm
5. 5.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
6. 6.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
7. 7.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
8. 8.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 3 times (c) 6 times (d) 27 times
9. 9.A cube has edges of 12 cm. What is its total surface area? (a) 144 sq cm (b) 864 sq cm (c) 576 sq cm (d) 1728 sq cm
10. 10.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) 125 times (d) 5 times
11. 11.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
12. 12.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
13. 13.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
14. 14.A cube has edges of 10 cm. What is its volume? (a) 30 cu cm (b) 1000 cu cm (c) 600 cu cm (d) 400 cu cm
15. 15.A cuboid is 9 cm long, 7 cm wide and 7 cm high. What is its volume? (a) 23 cu cm (b) 63 cu cm (c) 441 cu cm (d) 350 cu cm
16. 16.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 9 sq cm (c) 27 sq cm (d) 54 sq cm
17. 17.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
18. 18.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 3850 cm (d) 110 cm
19. 19.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
20. 20.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
21. 21.A cuboid is 8 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 184 sq cm (b) 92 sq cm (c) 48 sq cm (d) 46 sq cm
22. 22.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
23. 23.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
24. 24.A cuboid is 8 cm long, 4 cm wide and 4 cm high. What is its total surface area? (a) 320 sq cm (b) 128 sq cm (c) 80 sq cm (d) 160 sq cm
25. 25.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) 6 times (c) 4 times (d) 8 times
26. 26.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 25 times (c) 5 times (d) 10 times
27. 27.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 150 cu cm (c) 15 cu cm (d) 100 cu cm
28. 28.A cuboid is 8 cm long, 7 cm wide and 2 cm high. What is its total surface area? (a) 172 sq cm (b) 86 sq cm (c) 344 sq cm (d) 112 sq cm
29. 29.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
30. 30.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 384 cu cm (c) 24 cu cm (d) 512 cu cm
31. 31.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 26 sq cm (b) 104 sq cm (c) 24 sq cm (d) 52 sq cm
32. 32.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 49 sq cm (c) 294 sq cm (d) 343 sq cm
33. 33.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 726 cu cm (c) 1331 cu cm (d) 33 cu cm
34. 34.A cuboid is 9 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 128 sq cm (b) 512 sq cm (c) 256 sq cm (d) 180 sq cm
35. 35.A cuboid is 6 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 24 cu cm (b) 12 cu cm (c) 56 cu cm (d) 10 cu cm
36. 36.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 352 cm (d) 88 cm
37. 37.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
38. 38.A cuboid is 9 cm long, 7 cm wide and 2 cm high. What is its total surface area? (a) 95 sq cm (b) 126 sq cm (c) 380 sq cm (d) 190 sq cm
39. 39.A cuboid is 9 cm long, 8 cm wide and 8 cm high. What is its total surface area? (a) 416 sq cm (b) 208 sq cm (c) 832 sq cm (d) 576 sq cm
40. 40.If the side of a square 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

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