Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 68 · 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 diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 176 cm (d) 88 cm
2. 2.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) 4 times (c) 8 times (d) 5 times
3. 3.A cuboid is 4 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 104 sq cm (b) 24 sq cm (c) 52 sq cm (d) 26 sq cm
4. 4.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 121 sq cm (c) 484 sq cm (d) 726 sq cm
5. 5.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 9 times (c) 3 times (d) 27 times
6. 6.A cuboid is 5 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 110 sq cm (b) 55 sq cm (c) 220 sq cm (d) 75 sq cm
7. 7.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
8. 8.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 10 times (c) 125 times (d) 5 times
9. 9.A cuboid is 9 cm long, 8 cm wide and 10 cm high. What is its volume? (a) 27 cu cm (b) 484 cu cm (c) 72 cu cm (d) 720 cu cm
10. 10.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 46 sq cm (b) 48 sq cm (c) 92 sq cm (d) 184 sq cm
11. 11.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
12. 12.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 343 sq cm (c) 294 sq cm (d) 49 sq cm
13. 13.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
14. 14.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
15. 15.A cuboid is 9 cm long, 7 cm wide and 6 cm high. What is its volume? (a) 63 cu cm (b) 318 cu cm (c) 378 cu cm (d) 22 cu cm
16. 16.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
17. 17.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 82 cu cm (b) 6 cu cm (c) 42 cu cm (d) 12 cu cm
18. 18.A cuboid is 7 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 127 sq cm (b) 508 sq cm (c) 254 sq cm (d) 252 sq cm
19. 19.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) 6 times (c) 3 times (d) 27 times
20. 20.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) 16 times (d) 64 times
21. 21.A cuboid is 9 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 588 sq cm (b) 147 sq cm (c) 294 sq cm (d) 270 sq cm
22. 22.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 616 sq cm (d) 77 sq cm
23. 23.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 27 times (c) 3 times (d) 6 times
24. 24.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 256 sq cm (c) 384 sq cm (d) 64 sq cm
25. 25.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 16 times (c) 64 times (d) 8 times
26. 26.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
27. 27.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
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) 8 times (b) 5 times (c) 4 times (d) 2 times
29. 29.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 308 sq cm
30. 30.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
31. 31.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 1386 sq cm
32. 32.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 384 cu cm (c) 24 cu cm (d) 256 cu cm
33. 33.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
34. 34.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
35. 35.A cuboid is 5 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 13 cu cm (b) 110 cu cm (c) 75 cu cm (d) 15 cu cm
36. 36.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
37. 37.A cuboid is 9 cm long, 8 cm wide and 4 cm high. What is its total surface area? (a) 288 sq cm (b) 560 sq cm (c) 280 sq cm (d) 140 sq cm
38. 38.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 125 sq cm (c) 150 sq cm (d) 100 sq cm
39. 39.A cuboid is 5 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 15 cu cm (b) 78 cu cm (c) 45 cu cm (d) 11 cu cm
40. 40.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) 5 times (c) 25 times (d) 125 times

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