Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 237 · 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 every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 27 times (c) 6 times (d) 3 times
2. 2.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
3. 3.A cuboid is 10 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 69 sq cm (b) 276 sq cm (c) 90 sq cm (d) 138 sq cm
4. 4.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
5. 5.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 54 cu cm (c) 27 cu cm (d) 9 cu cm
6. 6.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 24 cu cm (c) 256 cu cm (d) 512 cu cm
7. 7.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
8. 8.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 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) 5 times (b) 4 times (c) 8 times (d) 2 times
10. 10.A cuboid is 9 cm long, 5 cm wide and 6 cm high. What is its total surface area? (a) 516 sq cm (b) 129 sq cm (c) 258 sq cm (d) 270 sq cm
11. 11.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
12. 12.A cuboid is 9 cm long, 8 cm wide and 4 cm high. What is its volume? (a) 72 cu cm (b) 288 cu cm (c) 21 cu cm (d) 280 cu cm
13. 13.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 176 cm (d) 44 cm
14. 14.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) 2 times (d) 4 times
15. 15.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) 4 times (d) 5 times
16. 16.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
17. 17.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 25 times (c) 10 times (d) 125 times
18. 18.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) 64 times (c) 16 times (d) 8 times
19. 19.A cube has edges of 12 cm. What is its volume? (a) 36 cu cm (b) 576 cu cm (c) 1728 cu cm (d) 864 cu cm
20. 20.A cuboid is 7 cm long, 6 cm wide and 4 cm high. What is its total surface area? (a) 188 sq cm (b) 168 sq cm (c) 376 sq cm (d) 94 sq cm
21. 21.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
22. 22.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
23. 23.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 96 cu cm (c) 64 cu cm (d) 12 cu cm
24. 24.A cuboid is 5 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 90 sq cm (b) 126 sq cm (c) 252 sq cm (d) 63 sq cm
25. 25.A cuboid is 12 cm long, 11 cm wide and 6 cm high. What is its total surface area? (a) 270 sq cm (b) 792 sq cm (c) 1080 sq cm (d) 540 sq cm
26. 26.A cube has edges of 9 cm. What is its volume? (a) 729 cu cm (b) 324 cu cm (c) 27 cu cm (d) 486 cu cm
27. 27.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 112 cu cm (b) 6 cu cm (c) 15 cu cm (d) 60 cu cm
28. 28.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
29. 29.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
30. 30.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 16 times (c) 64 times (d) 4 times
31. 31.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 1386 cm (d) 264 cm
32. 32.A cube has edges of 6 cm. What is its total surface area? (a) 217 sq cm (b) 216 sq cm (c) 144 sq cm (d) 36 sq cm
33. 33.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
34. 34.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 616 sq cm
35. 35.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 2464 cm (d) 352 cm
36. 36.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 2464 cm (d) 88 cm
37. 37.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
38. 38.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 9 times (c) 6 times (d) 3 times
39. 39.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
40. 40.A cuboid is 6 cm long, 4 cm wide and 5 cm high. What is its total surface area? (a) 120 sq cm (b) 74 sq cm (c) 296 sq cm (d) 148 sq cm

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