Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 662 · 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 4 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 16 sq cm (b) 20 sq cm (c) 40 sq cm (d) 80 sq cm
2. 2.A cube has edges of 11 cm. What is its volume? (a) 1331 cu cm (b) 726 cu cm (c) 484 cu cm (d) 33 cu cm
3. 3.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
4. 4.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 100 cu cm (c) 125 cu cm (d) 15 cu cm
5. 5.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 4 times (b) 8 times (c) 5 times (d) 2 times
6. 6.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 9856 sq cm
7. 7.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
8. 8.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
9. 9.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) 27 times (c) 3 times (d) 6 times
10. 10.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 693 sq cm
11. 11.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
12. 12.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 64 cu cm (c) 65 cu cm (d) 96 cu cm
13. 13.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
14. 14.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm
15. 15.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) 4 times (c) 8 times (d) 5 times
16. 16.A cuboid is 8 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 20 cu cm (b) 216 cu cm (c) 24 cu cm (d) 246 cu cm
17. 17.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
18. 18.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
19. 19.A cube has edges of 2 cm. What is its total surface area? (a) 24 sq cm (b) 16 sq cm (c) 8 sq cm (d) 4 sq cm
20. 20.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 88 cm (d) 22 cm
21. 21.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 88 cm (d) 2464 cm
22. 22.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 384 sq cm (c) 64 sq cm (d) 256 sq cm
23. 23.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 21 cu cm (c) 196 cu cm (d) 343 cu cm
24. 24.A cuboid is 12 cm long, 5 cm wide and 3 cm high. What is its total surface area? (a) 444 sq cm (b) 222 sq cm (c) 180 sq cm (d) 111 sq cm
25. 25.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
26. 26.A cuboid is 10 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 484 sq cm (b) 210 sq cm (c) 121 sq cm (d) 242 sq cm
27. 27.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) 27 times (c) 6 times (d) 9 times
28. 28.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
29. 29.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 4 times (c) 8 times (d) 16 times
30. 30.A cuboid is 10 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 216 cu cm (b) 180 cu cm (c) 30 cu cm (d) 19 cu cm
31. 31.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
32. 32.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
33. 33.A cuboid is 7 cm long, 4 cm wide and 3 cm high. What is its total surface area? (a) 84 sq cm (b) 61 sq cm (c) 244 sq cm (d) 122 sq cm
34. 34.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) 9 times (c) 3 times (d) 6 times
35. 35.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 44 cm (d) 176 cm
36. 36.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
37. 37.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 64 times (c) 4 times (d) 8 times
38. 38.A cuboid is 7 cm long, 6 cm wide and 4 cm high. What is its volume? (a) 42 cu cm (b) 17 cu cm (c) 188 cu cm (d) 168 cu cm
39. 39.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 2 times (c) 4 times (d) 6 times
40. 40.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 25 times (d) 10 times

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