Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 100 · 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) 176 cm (b) 2464 cm (c) 352 cm (d) 88 cm
2. 2.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 110 cm (d) 3850 cm
3. 3.A cube has edges of 11 cm. What is its total surface area? (a) 121 sq cm (b) 726 sq cm (c) 1331 sq cm (d) 484 sq cm
4. 4.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm
5. 5.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) 64 times (c) 16 times (d) 8 times
6. 6.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 6 times (c) 27 times (d) 9 times
7. 7.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
8. 8.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) 8 times (c) 5 times (d) 4 times
9. 9.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 512 cu cm (c) 384 cu cm (d) 24 cu cm
10. 10.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
11. 11.A cube has edges of 7 cm. What is its total surface area? (a) 294 sq cm (b) 196 sq cm (c) 49 sq cm (d) 343 sq cm
12. 12.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 22 cm (d) 44 cm
13. 13.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 36 cu cm (c) 1728 cu cm (d) 576 cu cm
14. 14.A cuboid is 11 cm long, 6 cm wide and 6 cm high. What is its total surface area? (a) 168 sq cm (b) 336 sq cm (c) 672 sq cm (d) 396 sq cm
15. 15.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
16. 16.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
17. 17.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
18. 18.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 52 cu cm (b) 24 cu cm (c) 9 cu cm (d) 6 cu cm
19. 19.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) 2 times (c) 8 times (d) 4 times
20. 20.A cuboid is 9 cm long, 5 cm wide and 7 cm high. What is its total surface area? (a) 143 sq cm (b) 286 sq cm (c) 315 sq cm (d) 572 sq cm
21. 21.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 24 cu cm (c) 6 cu cm (d) 16 cu cm
22. 22.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
23. 23.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
24. 24.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 220 cm (d) 440 cm
25. 25.A cube has edges of 5 cm. What is its volume? (a) 100 cu cm (b) 125 cu cm (c) 150 cu cm (d) 15 cu cm
26. 26.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 132 cm (d) 1386 cm
27. 27.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
28. 28.If the radius of a circle 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
29. 29.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) 27 times (c) 6 times (d) 9 times
30. 30.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 36 cu cm (c) 27 cu cm (d) 9 cu cm
31. 31.A cuboid is 12 cm long, 4 cm wide and 4 cm high. What is its total surface area? (a) 448 sq cm (b) 224 sq cm (c) 112 sq cm (d) 192 sq cm
32. 32.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 308 sq cm
33. 33.A cuboid is 10 cm long, 7 cm wide and 9 cm high. What is its total surface area? (a) 223 sq cm (b) 630 sq cm (c) 446 sq cm (d) 892 sq cm
34. 34.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
35. 35.A cuboid is 7 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 204 sq cm (b) 102 sq cm (c) 63 sq cm (d) 51 sq cm
36. 36.A cuboid is 8 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 97 cu cm (b) 96 cu cm (c) 152 cu cm (d) 16 cu cm
37. 37.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 10 times (c) 25 times (d) 5 times
38. 38.A cuboid is 4 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 200 sq cm (b) 56 sq cm (c) 100 sq cm (d) 50 sq cm
39. 39.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 1232 sq cm
40. 40.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm

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