Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 195 · 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 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
2. 2.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
3. 3.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) 16 times (c) 64 times (d) 8 times
4. 4.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
5. 5.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) 9 times (c) 27 times (d) 6 times
6. 6.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 31 sq cm (b) 62 sq cm (c) 30 sq cm (d) 124 sq cm
7. 7.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 616 sq cm (d) 77 sq cm
8. 8.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 4 times (c) 2 times (d) 8 times
9. 9.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
10. 10.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) 125 times (d) 10 times
11. 11.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 41 sq cm (b) 164 sq cm (c) 42 sq cm (d) 82 sq cm
12. 12.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
13. 13.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 6 cu cm (b) 42 cu cm (c) 8 cu cm (d) 18 cu cm
14. 14.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
15. 15.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
16. 16.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
17. 17.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
18. 18.A cuboid is 4 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 104 sq cm (b) 52 sq cm (c) 24 sq cm (d) 26 sq cm
19. 19.A cube has edges of 9 cm. What is its volume? (a) 486 cu cm (b) 27 cu cm (c) 729 cu cm (d) 324 cu cm
20. 20.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 64 times (c) 4 times (d) 8 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) 8 times (d) 4 times
22. 22.A cuboid is 8 cm long, 7 cm wide and 6 cm high. What is its volume? (a) 292 cu cm (b) 56 cu cm (c) 336 cu cm (d) 21 cu cm
23. 23.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) 10 times (c) 25 times (d) 125 times
24. 24.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
25. 25.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
26. 26.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) 9 times (c) 3 times (d) 6 times
27. 27.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
28. 28.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
29. 29.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) 5 times (c) 8 times (d) 2 times
30. 30.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 693 sq cm
31. 31.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 64 sq cm (c) 96 sq cm (d) 16 sq cm
32. 32.A cuboid is 6 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 144 sq cm (b) 288 sq cm (c) 72 sq cm (d) 108 sq cm
33. 33.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 12 sq cm (b) 32 sq cm (c) 16 sq cm (d) 64 sq cm
34. 34.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) 5 times (d) 2 times
35. 35.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 1386 cm (d) 66 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 cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 11 cu cm (b) 6 cu cm (c) 36 cu cm (d) 72 cu cm
38. 38.A cuboid is 7 cm long, 6 cm wide and 7 cm high. What is its volume? (a) 20 cu cm (b) 294 cu cm (c) 266 cu cm (d) 42 cu cm
39. 39.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 54 sq cm (c) 27 sq cm (d) 9 sq cm
40. 40.A cuboid is 6 cm long, 5 cm wide and 5 cm high. What is its total surface area? (a) 150 sq cm (b) 340 sq cm (c) 170 sq cm (d) 85 sq cm

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