Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 491 · 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 3 times as long, how many times as big does its area become? (a) 27 times (b) 9 times (c) 6 times (d) 3 times
2. 2.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 5 times (c) 8 times (d) 4 times
3. 3.A cube has edges of 5 cm. What is its total surface area? (a) 150 sq cm (b) 100 sq cm (c) 125 sq cm (d) 25 sq cm
4. 4.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
5. 5.A cuboid is 8 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 144 cu cm (b) 19 cu cm (c) 212 cu cm (d) 16 cu cm
6. 6.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
7. 7.A cuboid is 7 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 95 sq cm (b) 380 sq cm (c) 190 sq cm (d) 126 sq cm
8. 8.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 66 cm (d) 264 cm
9. 9.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 88 sq cm
10. 10.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq cm
11. 11.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) 6 times (c) 27 times (d) 3 times
12. 12.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
13. 13.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
14. 14.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
15. 15.A cuboid is 12 cm long, 4 cm wide and 4 cm high. What is its total surface area? (a) 224 sq cm (b) 448 sq cm (c) 192 sq cm (d) 112 sq cm
16. 16.If the radius of a circle 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
17. 17.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) 25 times (d) 5 times
18. 18.A cuboid is 10 cm long, 8 cm wide and 3 cm high. What is its volume? (a) 21 cu cm (b) 80 cu cm (c) 268 cu cm (d) 240 cu cm
19. 19.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) 5 times (c) 125 times (d) 10 times
20. 20.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 256 cu cm (c) 24 cu cm (d) 512 cu cm
21. 21.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
22. 22.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 3850 cm (d) 440 cm
23. 23.A cuboid is 9 cm long, 4 cm wide and 9 cm high. What is its volume? (a) 36 cu cm (b) 306 cu cm (c) 22 cu cm (d) 324 cu cm
24. 24.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
25. 25.A cube has edges of 6 cm. What is its total surface area? (a) 217 sq cm (b) 144 sq cm (c) 216 sq cm (d) 36 sq cm
26. 26.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) 8 times (d) 4 times
27. 27.A cuboid is 9 cm long, 4 cm wide and 8 cm high. What is its total surface area? (a) 280 sq cm (b) 288 sq cm (c) 140 sq cm (d) 560 sq cm
28. 28.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
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) 9 times (d) 6 times
30. 30.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 62 sq cm (b) 124 sq cm (c) 31 sq cm (d) 30 sq cm
31. 31.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
32. 32.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
33. 33.A cuboid is 10 cm long, 6 cm wide and 9 cm high. What is its total surface area? (a) 816 sq cm (b) 204 sq cm (c) 408 sq cm (d) 540 sq cm
34. 34.A cuboid is 7 cm long, 6 cm wide and 4 cm high. What is its total surface area? (a) 94 sq cm (b) 168 sq cm (c) 376 sq cm (d) 188 sq cm
35. 35.A cuboid is 7 cm long, 5 cm wide and 5 cm high. What is its total surface area? (a) 95 sq cm (b) 380 sq cm (c) 175 sq cm (d) 190 sq cm
36. 36.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
37. 37.A cube has edges of 12 cm. What is its total surface area? (a) 144 sq cm (b) 1728 sq cm (c) 864 sq cm (d) 576 sq cm
38. 38.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 4 sq cm (c) 24 sq cm (d) 16 sq cm
39. 39.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 9 times (c) 6 times (d) 27 times
40. 40.A cuboid is 4 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 120 sq cm (b) 164 sq cm (c) 328 sq cm (d) 82 sq cm

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