Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 61 · 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 diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
2. 2.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 693 sq cm
3. 3.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
4. 4.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) 27 times (c) 9 times (d) 6 times
5. 5.A cube has edges of 9 cm. What is its total surface area? (a) 486 sq cm (b) 81 sq cm (c) 729 sq cm (d) 324 sq cm
6. 6.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
7. 7.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 110 cm (d) 220 cm
8. 8.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
9. 9.A cuboid is 4 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 24 sq cm (b) 104 sq cm (c) 26 sq cm (d) 52 sq cm
10. 10.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
11. 11.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 308 sq cm (d) 2464 sq cm
12. 12.A cuboid is 11 cm long, 9 cm wide and 9 cm high. What is its total surface area? (a) 558 sq cm (b) 1116 sq cm (c) 891 sq cm (d) 279 sq cm
13. 13.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) 3 times (c) 9 times (d) 6 times
14. 14.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) 8 times (c) 2 times (d) 4 times
15. 15.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 64 times (d) 16 times
16. 16.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 2 times (c) 4 times (d) 5 times
17. 17.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
18. 18.A cuboid is 11 cm long, 8 cm wide and 8 cm high. What is its volume? (a) 27 cu cm (b) 88 cu cm (c) 704 cu cm (d) 480 cu cm
19. 19.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 44 sq cm (d) 616 sq cm
20. 20.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 125 times (c) 25 times (d) 10 times
21. 21.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
22. 22.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 352 cm (d) 2464 cm
23. 23.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) 8 times (c) 16 times (d) 64 times
24. 24.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 150 sq cm (c) 25 sq cm (d) 125 sq cm
25. 25.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
26. 26.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 1728 cu cm (c) 36 cu cm (d) 864 cu cm
27. 27.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) 6 times (c) 9 times (d) 3 times
28. 28.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times
29. 29.A cube has edges of 4 cm. What is its total surface area? (a) 96 sq cm (b) 64 sq cm (c) 97 sq cm (d) 16 sq cm
30. 30.A cuboid is 6 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 96 cu cm (b) 152 cu cm (c) 16 cu cm (d) 12 cu cm
31. 31.A cuboid is 9 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 254 cu cm (b) 36 cu cm (c) 252 cu cm (d) 20 cu cm
32. 32.A cuboid is 6 cm long, 4 cm wide and 5 cm high. What is its total surface area? (a) 120 sq cm (b) 296 sq cm (c) 74 sq cm (d) 148 sq cm
33. 33.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 24 sq cm (c) 4 sq cm (d) 8 sq cm
34. 34.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 36 cu cm (c) 54 cu cm (d) 9 cu cm
35. 35.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 1728 sq cm (c) 576 sq cm (d) 144 sq cm
36. 36.A cuboid is 9 cm long, 5 cm wide and 8 cm high. What is its volume? (a) 360 cu cm (b) 45 cu cm (c) 22 cu cm (d) 314 cu cm
37. 37.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 21 cu cm (c) 196 cu cm (d) 343 cu cm
38. 38.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) 125 times (c) 25 times (d) 5 times
39. 39.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 64 cu cm (b) 10 cu cm (c) 8 cu cm (d) 32 cu cm
40. 40.A cuboid is 12 cm long, 5 cm wide and 7 cm high. What is its volume? (a) 420 cu cm (b) 60 cu cm (c) 24 cu cm (d) 358 cu cm

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