Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 359 · 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 radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 10 times (c) 25 times (d) 125 times
2. 2.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 88 cm (d) 352 cm
3. 3.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
4. 4.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 24 cu cm (b) 6 cu cm (c) 52 cu cm (d) 9 cu cm
5. 5.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
6. 6.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
7. 7.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
8. 8.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 110 cm (d) 440 cm
9. 9.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
10. 10.A cube has edges of 12 cm. What is its volume? (a) 1728 cu cm (b) 864 cu cm (c) 576 cu cm (d) 36 cu cm
11. 11.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
12. 12.A cuboid is 4 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 84 cu cm (b) 14 cu cm (c) 12 cu cm (d) 122 cu cm
13. 13.A cuboid is 7 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 142 cu cm (b) 21 cu cm (c) 105 cu cm (d) 15 cu cm
14. 14.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 88 cm (d) 44 cm
15. 15.A cube has edges of 11 cm. What is its total surface area? (a) 484 sq cm (b) 121 sq cm (c) 1331 sq cm (d) 726 sq cm
16. 16.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
17. 17.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 176 sq cm
18. 18.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 22 cm (d) 88 cm
19. 19.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
20. 20.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
21. 21.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
22. 22.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 4 sq cm (c) 24 sq cm (d) 8 sq cm
23. 23.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 16 cu cm (c) 6 cu cm (d) 24 cu cm
24. 24.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 54 sq cm (c) 9 sq cm (d) 27 sq cm
25. 25.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
26. 26.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 15 cu cm (c) 150 cu cm (d) 100 cu cm
27. 27.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 2 times (d) 5 times
28. 28.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 4 times (b) 2 times (c) 5 times (d) 8 times
29. 29.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 6 times (c) 4 times (d) 2 times
30. 30.A cuboid is 6 cm long, 4 cm wide and 8 cm high. What is its total surface area? (a) 192 sq cm (b) 416 sq cm (c) 208 sq cm (d) 104 sq cm
31. 31.A cuboid is 8 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 224 sq cm (b) 56 sq cm (c) 64 sq cm (d) 112 sq cm
32. 32.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 25 times (b) 125 times (c) 10 times (d) 5 times
33. 33.A cuboid is 9 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 248 sq cm (b) 124 sq cm (c) 72 sq cm (d) 62 sq cm
34. 34.A cuboid is 7 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 111 sq cm (b) 222 sq cm (c) 444 sq cm (d) 189 sq cm
35. 35.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) 6 times (d) 27 times
36. 36.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 486 sq cm (c) 729 sq cm (d) 324 sq cm
37. 37.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 6 times (c) 9 times (d) 27 times
38. 38.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 4 times (c) 8 times (d) 64 times
39. 39.A cube has edges of 10 cm. What is its volume? (a) 30 cu cm (b) 400 cu cm (c) 600 cu cm (d) 1000 cu cm
40. 40.A cuboid is 4 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 56 sq cm (b) 50 sq cm (c) 200 sq cm (d) 100 sq cm

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