Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 249 · 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 area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 9856 sq cm
2. 2.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
3. 3.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
4. 4.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
5. 5.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) 125 times (c) 5 times (d) 10 times
6. 6.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 8 cu cm (b) 10 cu cm (c) 32 cu cm (d) 64 cu cm
7. 7.A cuboid is 6 cm long, 4 cm wide and 5 cm high. What is its total surface area? (a) 74 sq cm (b) 296 sq cm (c) 148 sq cm (d) 120 sq cm
8. 8.A cuboid is 5 cm long, 4 cm wide and 9 cm high. What is its volume? (a) 202 cu cm (b) 180 cu cm (c) 18 cu cm (d) 20 cu cm
9. 9.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
10. 10.A cuboid is 10 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 160 cu cm (b) 100 cu cm (c) 20 cu cm (d) 17 cu cm
11. 11.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm
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.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
14. 14.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 352 cm (d) 176 cm
15. 15.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
16. 16.A cube has edges of 10 cm. What is its total surface area? (a) 1000 sq cm (b) 100 sq cm (c) 600 sq cm (d) 400 sq cm
17. 17.A cuboid is 11 cm long, 9 cm wide and 4 cm high. What is its total surface area? (a) 716 sq cm (b) 396 sq cm (c) 179 sq cm (d) 358 sq cm
18. 18.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 616 cm (d) 44 cm
19. 19.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 27 cu cm (c) 54 cu cm (d) 9 cu cm
20. 20.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 616 sq cm (d) 77 sq cm
21. 21.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 6 times (c) 4 times (d) 8 times
22. 22.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 64 times (c) 4 times (d) 16 times
23. 23.A cuboid is 4 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 8 cu cm (b) 124 cu cm (c) 72 cu cm (d) 15 cu cm
24. 24.A cube has edges of 4 cm. What is its volume? (a) 64 cu cm (b) 65 cu cm (c) 96 cu cm (d) 12 cu cm
25. 25.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) 27 times (d) 6 times
26. 26.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
27. 27.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
28. 28.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 88 sq cm (d) 2464 sq cm
29. 29.A cuboid is 10 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 224 sq cm (b) 56 sq cm (c) 112 sq cm (d) 60 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) 64 times (b) 8 times (c) 16 times (d) 4 times
31. 31.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
32. 32.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) 8 times (d) 16 times
33. 33.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 16 times (c) 8 times (d) 64 times
34. 34.A cuboid is 10 cm long, 9 cm wide and 5 cm high. What is its volume? (a) 370 cu cm (b) 450 cu cm (c) 24 cu cm (d) 90 cu cm
35. 35.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 729 cu cm (c) 27 cu cm (d) 486 cu cm
36. 36.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) 3 times (d) 6 times
37. 37.A cube has edges of 11 cm. What is its total surface area? (a) 121 sq cm (b) 1331 sq cm (c) 484 sq cm (d) 726 sq cm
38. 38.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
39. 39.A cuboid is 11 cm long, 8 cm wide and 7 cm high. What is its total surface area? (a) 221 sq cm (b) 616 sq cm (c) 442 sq cm (d) 884 sq cm
40. 40.A cuboid is 4 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 12 cu cm (b) 15 cu cm (c) 96 cu cm (d) 136 cu cm

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