Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 111 · 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 5 times as long, how many times as big does its area become? (a) 125 times (b) 10 times (c) 5 times (d) 25 times
2. 2.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) 5 times (d) 8 times
3. 3.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
4. 4.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
5. 5.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
6. 6.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
7. 7.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 176 cm (d) 88 cm
8. 8.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 64 sq cm (b) 65 sq cm (c) 128 sq cm (d) 32 sq cm
9. 9.A cuboid is 7 cm long, 5 cm wide and 4 cm high. What is its volume? (a) 166 cu cm (b) 35 cu cm (c) 16 cu cm (d) 140 cu cm
10. 10.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
11. 11.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) 8 times (c) 64 times (d) 16 times
12. 12.A cube has edges of 7 cm. What is its volume? (a) 343 cu cm (b) 294 cu cm (c) 196 cu cm (d) 21 cu cm
13. 13.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
14. 14.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
15. 15.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
16. 16.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 616 sq cm (d) 88 sq cm
17. 17.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 1232 sq cm
18. 18.A cuboid is 6 cm long, 5 cm wide and 9 cm high. What is its total surface area? (a) 258 sq cm (b) 516 sq cm (c) 270 sq cm (d) 129 sq cm
19. 19.A cube has edges of 2 cm. What is its total surface area? (a) 4 sq cm (b) 24 sq cm (c) 16 sq cm (d) 8 sq cm
20. 20.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
21. 21.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
22. 22.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
23. 23.A cuboid is 11 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 33 cu cm (b) 23 cu cm (c) 318 cu cm (d) 297 cu cm
24. 24.A cube has edges of 6 cm. What is its total surface area? (a) 36 sq cm (b) 217 sq cm (c) 144 sq cm (d) 216 sq cm
25. 25.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 88 cm (d) 2464 cm
26. 26.If the radius of a circle 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
27. 27.A cuboid is 8 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 316 sq cm (b) 120 sq cm (c) 79 sq cm (d) 158 sq cm
28. 28.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 110 cm (d) 3850 cm
29. 29.A cuboid is 8 cm long, 7 cm wide and 4 cm high. What is its total surface area? (a) 116 sq cm (b) 232 sq cm (c) 224 sq cm (d) 464 sq cm
30. 30.A cube has edges of 12 cm. What is its total surface area? (a) 1728 sq cm (b) 576 sq cm (c) 144 sq cm (d) 864 sq cm
31. 31.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
32. 32.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
33. 33.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 44 cm (d) 616 cm
34. 34.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 64 sq cm (c) 96 sq cm (d) 97 sq cm
35. 35.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
36. 36.A cube has edges of 7 cm. What is its total surface area? (a) 343 sq cm (b) 49 sq cm (c) 294 sq cm (d) 196 sq cm
37. 37.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 36 cu cm (c) 9 cu cm (d) 54 cu cm
38. 38.A cuboid is 5 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 9 cu cm (b) 20 cu cm (c) 10 cu cm (d) 48 cu cm
39. 39.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
40. 40.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) 6 times (c) 2 times (d) 4 times

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