Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 645 · 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, 7 cm wide and 8 cm high. What is its total surface area? (a) 504 sq cm (b) 764 sq cm (c) 382 sq cm (d) 191 sq cm
2. 2.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
3. 3.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
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) 8 times (c) 5 times (d) 4 times
5. 5.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
6. 6.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
7. 7.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 110 cm (d) 220 cm
8. 8.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
9. 9.A cuboid is 9 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 20 cu cm (b) 27 cu cm (c) 216 cu cm (d) 246 cu cm
10. 10.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 3850 cm (d) 110 cm
11. 11.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 176 cm (d) 616 cm
12. 12.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
13. 13.A cuboid is 4 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 64 cu cm (b) 112 cu cm (c) 8 cu cm (d) 14 cu cm
14. 14.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
15. 15.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
16. 16.A cuboid is 10 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 88 sq cm (b) 44 sq cm (c) 40 sq cm (d) 176 sq cm
17. 17.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
18. 18.A cube has edges of 12 cm. What is its volume? (a) 1728 cu cm (b) 36 cu cm (c) 576 cu cm (d) 864 cu cm
19. 19.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 9 times (c) 3 times (d) 27 times
20. 20.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
21. 21.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
22. 22.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) 4 times (c) 2 times (d) 5 times
23. 23.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
24. 24.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 343 sq cm (c) 49 sq cm (d) 294 sq cm
25. 25.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) 10 times (d) 5 times
26. 26.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
27. 27.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 82 cu cm (b) 42 cu cm (c) 6 cu cm (d) 12 cu cm
28. 28.A cuboid is 7 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 416 sq cm (b) 208 sq cm (c) 140 sq cm (d) 104 sq cm
29. 29.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 51 sq cm (b) 54 sq cm (c) 102 sq cm (d) 204 sq cm
30. 30.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 64 times (d) 16 times
31. 31.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
32. 32.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) 8 times (c) 5 times (d) 4 times
33. 33.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 132 cm (d) 1386 cm
34. 34.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
35. 35.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 352 cm (d) 176 cm
36. 36.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 486 cu cm (c) 27 cu cm (d) 729 cu cm
37. 37.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 4 times (c) 6 times (d) 8 times
38. 38.A cuboid is 11 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 17 cu cm (b) 22 cu cm (c) 148 cu cm (d) 88 cu cm
39. 39.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) 25 times (c) 10 times (d) 5 times
40. 40.A cuboid is 6 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 13 cu cm (b) 12 cu cm (c) 60 cu cm (d) 104 cu cm

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