Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 847 · 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 volume become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
2. 2.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
3. 3.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 400 cu cm (c) 30 cu cm (d) 1000 cu cm
4. 4.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
5. 5.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
6. 6.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
7. 7.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
8. 8.A cuboid is 7 cm long, 6 cm wide and 10 cm high. What is its total surface area? (a) 172 sq cm (b) 420 sq cm (c) 344 sq cm (d) 688 sq cm
9. 9.A cuboid is 6 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 24 cu cm (b) 13 cu cm (c) 72 cu cm (d) 108 cu cm
10. 10.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
11. 11.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
12. 12.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
13. 13.A cube has edges of 5 cm. What is its volume? (a) 100 cu cm (b) 150 cu cm (c) 125 cu cm (d) 15 cu cm
14. 14.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 6 times (c) 3 times (d) 9 times
15. 15.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 256 cu cm (c) 512 cu cm (d) 384 cu cm
16. 16.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 8 times (c) 4 times (d) 16 times
17. 17.A cuboid is 9 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 36 cu cm (b) 72 cu cm (c) 124 cu cm (d) 15 cu cm
18. 18.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
19. 19.A cuboid is 9 cm long, 7 cm wide and 10 cm high. What is its volume? (a) 446 cu cm (b) 63 cu cm (c) 630 cu cm (d) 26 cu cm
20. 20.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) 3 times (c) 6 times (d) 9 times
21. 21.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) 16 times (c) 4 times (d) 8 times
22. 22.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 44 cm (d) 616 cm
23. 23.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 8 sq cm (c) 24 sq cm (d) 4 sq cm
24. 24.A cuboid is 8 cm long, 6 cm wide and 9 cm high. What is its volume? (a) 48 cu cm (b) 23 cu cm (c) 348 cu cm (d) 432 cu cm
25. 25.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
26. 26.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
27. 27.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 616 sq cm
28. 28.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
29. 29.A cuboid is 5 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 160 cu cm (b) 100 cu cm (c) 10 cu cm (d) 17 cu cm
30. 30.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
31. 31.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) 2 times (c) 8 times (d) 4 times
32. 32.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 25 times (c) 5 times (d) 125 times
33. 33.A cuboid is 4 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 56 sq cm (b) 200 sq cm (c) 100 sq cm (d) 50 sq cm
34. 34.A cuboid is 12 cm long, 8 cm wide and 3 cm high. What is its volume? (a) 96 cu cm (b) 23 cu cm (c) 312 cu cm (d) 288 cu cm
35. 35.A cuboid is 6 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 396 sq cm (b) 162 sq cm (c) 99 sq cm (d) 198 sq cm
36. 36.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 40 cu cm (b) 17 cu cm (c) 8 cu cm (d) 16 cu cm
37. 37.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
38. 38.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
39. 39.A cuboid is 6 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 24 sq cm (b) 28 sq cm (c) 56 sq cm (d) 112 sq cm
40. 40.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

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