Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 245 · 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 3 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 32 sq cm (b) 16 sq cm (c) 64 sq cm (d) 12 sq cm
2. 2.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 264 cm (d) 1386 cm
3. 3.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
4. 4.A cuboid is 6 cm long, 5 cm wide and 9 cm high. What is its volume? (a) 30 cu cm (b) 270 cu cm (c) 20 cu cm (d) 258 cu cm
5. 5.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) 27 times (d) 9 times
6. 6.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
7. 7.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
8. 8.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 1232 sq cm
9. 9.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 16 sq cm (c) 64 sq cm (d) 96 sq cm
10. 10.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 125 times (c) 5 times (d) 10 times
11. 11.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 27 sq cm (c) 54 sq cm (d) 36 sq cm
12. 12.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
13. 13.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
14. 14.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 18 sq cm (b) 21 sq cm (c) 42 sq cm (d) 84 sq cm
15. 15.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) 25 times (c) 5 times (d) 10 times
16. 16.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
17. 17.A cube has edges of 4 cm. What is its volume? (a) 64 cu cm (b) 12 cu cm (c) 96 cu cm (d) 65 cu cm
18. 18.A cuboid is 10 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 68 sq cm (b) 80 sq cm (c) 272 sq cm (d) 136 sq cm
19. 19.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 8 times (d) 4 times
20. 20.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
21. 21.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
22. 22.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 10 times (c) 5 times (d) 25 times
23. 23.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 176 cm (d) 88 cm
24. 24.A cuboid is 10 cm long, 5 cm wide and 8 cm high. What is its total surface area? (a) 400 sq cm (b) 340 sq cm (c) 680 sq cm (d) 170 sq cm
25. 25.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 16 cu cm (c) 6 cu cm (d) 8 cu cm
26. 26.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
27. 27.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm
28. 28.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 176 cm (d) 88 cm
29. 29.A cuboid is 5 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 252 sq cm (b) 126 sq cm (c) 63 sq cm (d) 90 sq cm
30. 30.A cuboid is 9 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 588 sq cm (b) 147 sq cm (c) 270 sq cm (d) 294 sq cm
31. 31.A cuboid is 5 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 62 sq cm (b) 31 sq cm (c) 124 sq cm (d) 30 sq cm
32. 32.A cuboid is 5 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 60 sq cm (b) 104 sq cm (c) 52 sq cm (d) 208 sq cm
33. 33.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 125 cu cm (c) 150 cu cm (d) 100 cu cm
34. 34.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) 3 times (d) 27 times
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) 9 times (c) 27 times (d) 3 times
36. 36.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
37. 37.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
38. 38.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 216 cu cm (c) 144 cu cm (d) 217 cu cm
39. 39.A cuboid is 9 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 19 cu cm (b) 189 cu cm (c) 27 cu cm (d) 222 cu cm
40. 40.A cuboid is 10 cm long, 4 cm wide and 5 cm high. What is its volume? (a) 40 cu cm (b) 220 cu cm (c) 19 cu cm (d) 200 cu cm

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