Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 375 · 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.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
2. 2.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 132 sq cm
3. 3.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 8 cu cm (b) 18 cu cm (c) 6 cu cm (d) 42 cu cm
4. 4.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
5. 5.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 144 sq cm (c) 217 sq cm (d) 36 sq cm
6. 6.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 2464 cm (d) 88 cm
7. 7.A cube has edges of 11 cm. What is its volume? (a) 1331 cu cm (b) 484 cu cm (c) 726 cu cm (d) 33 cu cm
8. 8.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 512 sq cm (c) 256 sq cm (d) 384 sq cm
9. 9.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
10. 10.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) 27 times (c) 9 times (d) 6 times
11. 11.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
12. 12.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 110 cm (d) 3850 cm
13. 13.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
14. 14.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
15. 15.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
16. 16.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 22 cm (d) 44 cm
17. 17.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
18. 18.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 30 cu cm (c) 1000 cu cm (d) 400 cu cm
19. 19.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 616 sq cm
20. 20.A cuboid is 11 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 608 sq cm (b) 304 sq cm (c) 220 sq cm (d) 152 sq cm
21. 21.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 616 sq cm
22. 22.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
23. 23.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) 3 times (c) 27 times (d) 9 times
24. 24.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
25. 25.A cuboid is 12 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 36 cu cm (b) 20 cu cm (c) 180 cu cm (d) 222 cu cm
26. 26.If the radius of a circle 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
27. 27.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 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 5 times as long, how many times as big does its volume become? (a) 25 times (b) 125 times (c) 10 times (d) 5 times
30. 30.A cuboid is 5 cm long, 4 cm wide and 8 cm high. What is its volume? (a) 17 cu cm (b) 20 cu cm (c) 184 cu cm (d) 160 cu cm
31. 31.A cuboid is 5 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 118 sq cm (b) 59 sq cm (c) 236 sq cm (d) 70 sq cm
32. 32.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 4 times (d) 8 times
33. 33.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 25 times (b) 5 times (c) 10 times (d) 125 times
34. 34.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 8 times (c) 6 times (d) 2 times
35. 35.A cuboid is 11 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 179 sq cm (b) 358 sq cm (c) 396 sq cm (d) 716 sq cm
36. 36.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 25 times (c) 10 times (d) 125 times
37. 37.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 352 cm (d) 88 cm
38. 38.A cube has edges of 6 cm. What is its volume? (a) 216 cu cm (b) 144 cu cm (c) 18 cu cm (d) 217 cu cm
39. 39.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 27 sq cm (c) 36 sq cm (d) 54 sq cm
40. 40.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 36 cu cm (c) 864 cu cm (d) 1728 cu cm

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