Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 473 · 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.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 64 sq cm (c) 256 sq cm (d) 384 sq cm
2. 2.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 15 cu cm (c) 100 cu cm (d) 150 cu cm
3. 3.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
4. 4.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 729 sq cm (c) 324 sq cm (d) 486 sq cm
5. 5.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
6. 6.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 1386 cm (d) 264 cm
7. 7.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 64 sq cm (c) 96 sq cm (d) 97 sq cm
8. 8.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) 6 times (c) 27 times (d) 9 times
9. 9.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
10. 10.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 64 times (c) 4 times (d) 8 times
11. 11.A cuboid is 10 cm long, 9 cm wide and 4 cm high. What is its total surface area? (a) 166 sq cm (b) 360 sq cm (c) 664 sq cm (d) 332 sq cm
12. 12.A cube has edges of 6 cm. What is its total surface area? (a) 217 sq cm (b) 144 sq cm (c) 216 sq cm (d) 36 sq cm
13. 13.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
14. 14.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
15. 15.A cuboid is 10 cm long, 5 cm wide and 5 cm high. What is its total surface area? (a) 251 sq cm (b) 250 sq cm (c) 125 sq cm (d) 500 sq cm
16. 16.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
17. 17.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
18. 18.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
19. 19.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 176 sq cm
20. 20.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 220 cm (d) 3850 cm
21. 21.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
22. 22.If the side of a square 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
23. 23.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
24. 24.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) 64 times (c) 8 times (d) 16 times
25. 25.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
26. 26.A cuboid is 6 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 168 sq cm (b) 108 sq cm (c) 336 sq cm (d) 84 sq cm
27. 27.A cuboid is 4 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 9 cu cm (b) 24 cu cm (c) 12 cu cm (d) 52 cu cm
28. 28.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 27 times (c) 3 times (d) 6 times
29. 29.A cuboid is 5 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 94 cu cm (b) 60 cu cm (c) 12 cu cm (d) 20 cu cm
30. 30.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
31. 31.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
32. 32.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
33. 33.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 9 cu cm (c) 27 cu cm (d) 36 cu cm
34. 34.A cube has edges of 2 cm. What is its total surface area? (a) 24 sq cm (b) 8 sq cm (c) 4 sq cm (d) 16 sq cm
35. 35.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
36. 36.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 52 cu cm (b) 6 cu cm (c) 9 cu cm (d) 24 cu cm
37. 37.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
38. 38.A cuboid is 5 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 264 sq cm (b) 132 sq cm (c) 66 sq cm (d) 80 sq cm
39. 39.A cuboid is 6 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 168 cu cm (b) 188 cu cm (c) 24 cu cm (d) 17 cu cm
40. 40.A cuboid is 5 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 120 cu cm (b) 16 cu cm (c) 158 cu cm (d) 15 cu cm

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