Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 545 · 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 radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
2. 2.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 600 cu cm (c) 30 cu cm (d) 400 cu cm
3. 3.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 77 sq cm (d) 44 sq cm
4. 4.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) 8 times (c) 4 times (d) 2 times
5. 5.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
6. 6.A cuboid is 11 cm long, 10 cm wide and 3 cm high. What is its total surface area? (a) 692 sq cm (b) 173 sq cm (c) 346 sq cm (d) 330 sq cm
7. 7.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 8 times (c) 2 times (d) 4 times
8. 8.A cuboid is 9 cm long, 6 cm wide and 9 cm high. What is its total surface area? (a) 378 sq cm (b) 189 sq cm (c) 486 sq cm (d) 756 sq cm
9. 9.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times
10. 10.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 16 sq cm (c) 24 sq cm (d) 4 sq cm
11. 11.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 352 cm (d) 2464 cm
12. 12.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) 16 times (c) 8 times (d) 64 times
13. 13.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) 5 times (c) 125 times (d) 10 times
14. 14.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) 5 times (c) 25 times (d) 10 times
15. 15.A cuboid is 11 cm long, 10 cm wide and 8 cm high. What is its total surface area? (a) 278 sq cm (b) 880 sq cm (c) 1112 sq cm (d) 556 sq cm
16. 16.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
17. 17.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 616 cm (d) 176 cm
18. 18.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
19. 19.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
20. 20.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 132 cm (d) 264 cm
21. 21.A cuboid is 11 cm long, 8 cm wide and 5 cm high. What is its volume? (a) 24 cu cm (b) 440 cu cm (c) 366 cu cm (d) 88 cu cm
22. 22.A cuboid is 7 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 190 sq cm (b) 126 sq cm (c) 95 sq cm (d) 380 sq cm
23. 23.A cube has edges of 11 cm. What is its volume? (a) 726 cu cm (b) 484 cu cm (c) 1331 cu cm (d) 33 cu cm
24. 24.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
25. 25.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) 16 times (d) 64 times
26. 26.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
27. 27.A cuboid is 5 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 118 cu cm (b) 14 cu cm (c) 70 cu cm (d) 10 cu cm
28. 28.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
29. 29.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
30. 30.A cube has edges of 6 cm. What is its volume? (a) 144 cu cm (b) 216 cu cm (c) 217 cu cm (d) 18 cu cm
31. 31.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 81 sq cm (c) 486 sq cm (d) 729 sq cm
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) 6 times (b) 9 times (c) 27 times (d) 3 times
33. 33.A cuboid is 4 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 72 sq cm (b) 108 sq cm (c) 216 sq cm (d) 54 sq cm
34. 34.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 352 cm (d) 176 cm
35. 35.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
36. 36.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) 64 times (c) 16 times (d) 8 times
37. 37.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
38. 38.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 96 sq cm (c) 97 sq cm (d) 16 sq cm
39. 39.A cuboid is 6 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 198 cu cm (b) 163 cu cm (c) 162 cu cm (d) 18 cu cm
40. 40.A cuboid is 9 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 27 cu cm (b) 19 cu cm (c) 189 cu cm (d) 222 cu cm

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