Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 294 · 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 cuboid is 5 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 188 sq cm (b) 47 sq cm (c) 60 sq cm (d) 94 sq cm
2. 2.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
3. 3.A cuboid is 4 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 72 cu cm (b) 13 cu cm (c) 12 cu cm (d) 108 cu cm
4. 4.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 12 cu cm (b) 7 cu cm (c) 6 cu cm (d) 32 cu 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) 27 times (b) 6 times (c) 9 times (d) 3 times
6. 6.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
7. 7.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
8. 8.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 2464 cm (d) 88 cm
9. 9.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
10. 10.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
11. 11.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) 4 times (c) 64 times (d) 16 times
12. 12.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 110 cm (d) 440 cm
13. 13.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
14. 14.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 16 cu cm (c) 24 cu cm (d) 8 cu cm
15. 15.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
16. 16.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
17. 17.A cuboid is 6 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 240 sq cm (b) 124 sq cm (c) 496 sq cm (d) 248 sq cm
18. 18.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 2464 cm (d) 352 cm
19. 19.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) 3 times (c) 6 times (d) 9 times
20. 20.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
21. 21.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 125 sq cm (c) 100 sq cm (d) 150 sq cm
22. 22.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 3850 cm (d) 110 cm
23. 23.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 6 times (c) 27 times (d) 3 times
24. 24.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
25. 25.A cuboid is 12 cm long, 10 cm wide and 9 cm high. What is its total surface area? (a) 318 sq cm (b) 1080 sq cm (c) 636 sq cm (d) 1272 sq cm
26. 26.A cuboid is 4 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 9 cu cm (b) 8 cu cm (c) 52 cu cm (d) 24 cu cm
27. 27.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
28. 28.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
29. 29.A cuboid is 7 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 208 cu cm (b) 19 cu cm (c) 140 cu cm (d) 14 cu cm
30. 30.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 144 sq cm (c) 1728 sq cm (d) 864 sq cm
31. 31.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 125 times (b) 10 times (c) 5 times (d) 25 times
32. 32.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
33. 33.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
34. 34.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) 8 times (c) 4 times (d) 2 times
35. 35.A cuboid is 5 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 20 cu cm (b) 10 cu cm (c) 9 cu cm (d) 48 cu cm
36. 36.A cuboid is 10 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 44 sq cm (b) 176 sq cm (c) 88 sq cm (d) 40 sq cm
37. 37.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 343 cu cm (c) 294 cu cm (d) 196 cu cm
38. 38.A cube has edges of 6 cm. What is its volume? (a) 144 cu cm (b) 217 cu cm (c) 18 cu cm (d) 216 cu cm
39. 39.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
40. 40.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times

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