Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 10 · 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 3 cm. What is its total surface area? (a) 27 sq cm (b) 54 sq cm (c) 9 sq cm (d) 36 sq cm
2. 2.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
3. 3.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
4. 4.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
5. 5.A cuboid is 6 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 176 sq cm (b) 48 sq cm (c) 44 sq cm (d) 88 sq cm
6. 6.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
7. 7.A cuboid is 6 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 126 sq cm (b) 162 sq cm (c) 324 sq cm (d) 81 sq cm
8. 8.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 2464 cm (d) 88 cm
9. 9.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
10. 10.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) 125 times (c) 25 times (d) 5 times
11. 11.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
12. 12.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 264 cm (d) 66 cm
13. 13.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) 64 times (c) 4 times (d) 16 times
14. 14.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 44 cm (d) 616 cm
15. 15.A cuboid is 10 cm long, 7 cm wide and 6 cm high. What is its total surface area? (a) 420 sq cm (b) 688 sq cm (c) 344 sq cm (d) 172 sq cm
16. 16.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 8 cu cm (c) 6 cu cm (d) 24 cu cm
17. 17.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
18. 18.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 2 times (c) 5 times (d) 8 times
19. 19.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 616 sq cm (d) 77 sq cm
20. 20.A cuboid is 5 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 380 sq cm (b) 150 sq cm (c) 95 sq cm (d) 190 sq cm
21. 21.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 132 sq cm
22. 22.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) 125 times (c) 25 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) 1232 sq cm (c) 2464 sq cm (d) 9856 sq cm
24. 24.A cuboid is 7 cm long, 5 cm wide and 2 cm high. What is its volume? (a) 14 cu cm (b) 118 cu cm (c) 35 cu cm (d) 70 cu cm
25. 25.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 4 sq cm (c) 16 sq cm (d) 24 sq cm
26. 26.A cube has edges of 7 cm. What is its total surface area? (a) 49 sq cm (b) 294 sq cm (c) 343 sq cm (d) 196 sq cm
27. 27.A cuboid is 11 cm long, 5 cm wide and 9 cm high. What is its volume? (a) 398 cu cm (b) 55 cu cm (c) 25 cu cm (d) 495 cu cm
28. 28.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
29. 29.If the radius of a circle 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
30. 30.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 616 sq cm
31. 31.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 44 sq cm (d) 77 sq cm
32. 32.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 9856 sq cm
33. 33.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) 8 times (c) 6 times (d) 4 times
34. 34.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) 9 times (d) 27 times
35. 35.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 4 times (c) 2 times (d) 5 times
36. 36.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 3 times (c) 9 times (d) 6 times
37. 37.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 110 cm (d) 220 cm
38. 38.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 4 times (c) 8 times (d) 64 times
39. 39.A cuboid is 5 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 38 sq cm (b) 40 sq cm (c) 76 sq cm (d) 152 sq cm
40. 40.A cuboid is 11 cm long, 6 cm wide and 3 cm high. What is its total surface area? (a) 117 sq cm (b) 234 sq cm (c) 468 sq cm (d) 198 sq cm

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