Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 303 · 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 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
2. 2.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
3. 3.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 48 sq cm (b) 184 sq cm (c) 92 sq cm (d) 46 sq cm
4. 4.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
5. 5.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 8 times (c) 4 times (d) 16 times
6. 6.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 220 cm (d) 3850 cm
7. 7.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 77 sq cm (d) 616 sq cm
8. 8.A cuboid is 7 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 41 sq cm (b) 164 sq cm (c) 42 sq cm (d) 82 sq cm
9. 9.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
10. 10.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
11. 11.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
12. 12.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
13. 13.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) 6 times (d) 9 times
14. 14.A cuboid is 8 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 246 sq cm (b) 123 sq cm (c) 216 sq cm (d) 492 sq 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) 5 times (b) 2 times (c) 4 times (d) 8 times
16. 16.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
17. 17.If the side of a square 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
18. 18.What is the area of a circle of diameter 14 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 circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
20. 20.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 22 cm (d) 88 cm
21. 21.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
22. 22.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) 8 times (c) 4 times (d) 2 times
23. 23.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 5 times (c) 125 times (d) 10 times
24. 24.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 8 times (c) 4 times (d) 64 times
25. 25.A cuboid is 5 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 118 cu cm (b) 10 cu cm (c) 14 cu cm (d) 70 cu cm
26. 26.A cuboid is 11 cm long, 5 cm wide and 8 cm high. What is its volume? (a) 55 cu cm (b) 24 cu cm (c) 366 cu cm (d) 440 cu cm
27. 27.A cuboid is 8 cm long, 5 cm wide and 4 cm high. What is its volume? (a) 40 cu cm (b) 184 cu cm (c) 160 cu cm (d) 17 cu cm
28. 28.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
29. 29.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
30. 30.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 97 sq cm (c) 96 sq cm (d) 64 sq cm
31. 31.A cube has edges of 8 cm. What is its total surface area? (a) 384 sq cm (b) 64 sq cm (c) 512 sq cm (d) 256 sq cm
32. 32.A cuboid is 12 cm long, 10 cm wide and 10 cm high. What is its volume? (a) 120 cu cm (b) 32 cu cm (c) 1200 cu cm (d) 680 cu cm
33. 33.A cube has edges of 7 cm. What is its total surface area? (a) 49 sq cm (b) 343 sq cm (c) 294 sq cm (d) 196 sq cm
34. 34.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 352 cm (d) 176 cm
35. 35.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 88 cm (d) 22 cm
36. 36.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) 8 times (d) 6 times
37. 37.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) 10 times (c) 25 times (d) 5 times
38. 38.A cuboid is 10 cm long, 5 cm wide and 5 cm high. What is its total surface area? (a) 250 sq cm (b) 251 sq cm (c) 500 sq cm (d) 125 sq cm
39. 39.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 324 cu cm (c) 486 cu cm (d) 729 cu cm
40. 40.A cuboid is 9 cm long, 6 cm wide and 4 cm high. What is its volume? (a) 228 cu cm (b) 19 cu cm (c) 54 cu cm (d) 216 cu cm

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