Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 299 · 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 9 cm long, 5 cm wide and 6 cm high. What is its volume? (a) 20 cu cm (b) 258 cu cm (c) 270 cu cm (d) 45 cu cm
2. 2.A cuboid is 12 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 324 sq cm (b) 162 sq cm (c) 81 sq cm (d) 108 sq cm
3. 3.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
4. 4.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) 5 times (c) 8 times (d) 4 times
5. 5.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
6. 6.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 176 cm (d) 88 cm
7. 7.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
8. 8.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
9. 9.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
10. 10.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
11. 11.A cuboid is 7 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 28 cu cm (b) 280 cu cm (c) 21 cu cm (d) 276 cu cm
12. 12.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
13. 13.A cuboid is 10 cm long, 7 cm wide and 2 cm high. What is its total surface area? (a) 416 sq cm (b) 104 sq cm (c) 208 sq cm (d) 140 sq cm
14. 14.A cuboid is 12 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 96 sq cm (b) 160 sq cm (c) 80 sq cm (d) 320 sq cm
15. 15.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 36 sq cm (c) 217 sq cm (d) 144 sq cm
16. 16.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
17. 17.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
18. 18.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 44 sq cm (d) 616 sq cm
19. 19.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
20. 20.A cuboid is 4 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 38 sq cm (b) 40 sq cm (c) 76 sq cm (d) 152 sq cm
21. 21.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
22. 22.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
23. 23.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 8 times (c) 4 times (d) 2 times
24. 24.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
25. 25.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
26. 26.A cuboid is 7 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 84 cu cm (b) 28 cu cm (c) 122 cu cm (d) 14 cu cm
27. 27.A cuboid is 8 cm long, 6 cm wide and 4 cm high. What is its volume? (a) 192 cu cm (b) 208 cu cm (c) 18 cu cm (d) 48 cu cm
28. 28.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
29. 29.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
30. 30.A cuboid is 4 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 54 sq cm (b) 216 sq cm (c) 72 sq cm (d) 108 sq cm
31. 31.If the side of a square 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
32. 32.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) 64 times (c) 4 times (d) 16 times
33. 33.A cuboid is 8 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 112 cu cm (b) 64 cu cm (c) 32 cu cm (d) 14 cu cm
34. 34.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 32 sq cm (b) 128 sq cm (c) 64 sq cm (d) 65 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) 9 times (b) 3 times (c) 6 times (d) 27 times
36. 36.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
37. 37.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
38. 38.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) 27 times (c) 3 times (d) 6 times
39. 39.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 176 sq cm
40. 40.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 125 cu cm (c) 100 cu cm (d) 150 cu cm

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