Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 921 · 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 5 cm. What is its volume? (a) 15 cu cm (b) 150 cu cm (c) 100 cu cm (d) 125 cu cm
2. 2.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 150 sq cm (c) 125 sq cm (d) 100 sq cm
3. 3.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
4. 4.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
5. 5.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
6. 6.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 616 cm (d) 176 cm
7. 7.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 3850 cm (d) 110 cm
8. 8.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) 25 times (c) 125 times (d) 5 times
9. 9.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
10. 10.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
11. 11.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
12. 12.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) 64 times (d) 4 times
13. 13.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 440 cm (d) 110 cm
14. 14.A cube has edges of 10 cm. What is its volume? (a) 400 cu cm (b) 1000 cu cm (c) 600 cu cm (d) 30 cu cm
15. 15.A cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 1000 sq cm (c) 400 sq cm (d) 100 sq cm
16. 16.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) 9 times (c) 3 times (d) 27 times
17. 17.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 88 cm (d) 352 cm
18. 18.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
19. 19.A cube has edges of 6 cm. What is its volume? (a) 144 cu cm (b) 216 cu cm (c) 217 cu cm (d) 18 cu cm
20. 20.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
21. 21.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 616 sq cm (d) 88 sq cm
22. 22.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 104 sq cm (b) 24 sq cm (c) 52 sq cm (d) 26 sq cm
23. 23.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 4 times (c) 5 times (d) 8 times
24. 24.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 81 sq cm (c) 486 sq cm (d) 324 sq cm
25. 25.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
26. 26.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 2 times (d) 5 times
27. 27.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
28. 28.A cube has edges of 11 cm. What is its volume? (a) 726 cu cm (b) 484 cu cm (c) 1331 cu cm (d) 33 cu cm
29. 29.A cuboid is 7 cm long, 6 cm wide and 10 cm high. What is its volume? (a) 23 cu cm (b) 420 cu cm (c) 344 cu cm (d) 42 cu cm
30. 30.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
31. 31.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
32. 32.A cube has edges of 7 cm. What is its total surface area? (a) 294 sq cm (b) 49 sq cm (c) 343 sq cm (d) 196 sq cm
33. 33.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) 16 times (c) 8 times (d) 64 times
34. 34.A cube has edges of 11 cm. What is its total surface area? (a) 726 sq cm (b) 121 sq cm (c) 484 sq cm (d) 1331 sq cm
35. 35.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
36. 36.A cuboid is 4 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 122 sq cm (b) 244 sq cm (c) 61 sq cm (d) 84 sq cm
37. 37.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
38. 38.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 24 cu cm (c) 16 cu cm (d) 8 cu cm
39. 39.A cuboid is 5 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 158 cu cm (b) 15 cu cm (c) 16 cu cm (d) 120 cu cm
40. 40.A cuboid is 4 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 216 sq cm (b) 108 sq cm (c) 54 sq cm (d) 72 sq cm

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