Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 323 · 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) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
2. 2.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
3. 3.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm
4. 4.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
5. 5.If the side of a square 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
6. 6.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
7. 7.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 693 sq cm
8. 8.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
9. 9.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 176 cm (d) 88 cm
10. 10.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 4 times (c) 8 times (d) 16 times
11. 11.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
12. 12.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
13. 13.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
14. 14.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
15. 15.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
16. 16.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
17. 17.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 5 times (c) 2 times (d) 8 times
18. 18.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
19. 19.A cuboid is 5 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 174 cu cm (b) 15 cu cm (c) 17 cu cm (d) 135 cu cm
20. 20.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
21. 21.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) 125 times (c) 5 times (d) 10 times
22. 22.A cuboid is 5 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 30 sq cm (b) 31 sq cm (c) 62 sq cm (d) 124 sq cm
23. 23.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) 8 times (c) 4 times (d) 16 times
24. 24.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
25. 25.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) 64 times (c) 16 times (d) 8 times
26. 26.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 16 times (d) 64 times
27. 27.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
28. 28.A cuboid is 6 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 228 sq cm (b) 456 sq cm (c) 216 sq cm (d) 114 sq cm
29. 29.A cuboid is 6 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 13 cu cm (b) 72 cu cm (c) 108 cu cm (d) 18 cu cm
30. 30.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 15 cu cm (c) 100 cu cm (d) 150 cu cm
31. 31.A cuboid is 4 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 9 cu cm (b) 12 cu cm (c) 52 cu cm (d) 24 cu cm
32. 32.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 6 times (c) 27 times (d) 9 times
33. 33.A cuboid is 7 cm long, 6 cm wide and 8 cm high. What is its volume? (a) 336 cu cm (b) 21 cu cm (c) 42 cu cm (d) 292 cu cm
34. 34.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) 4 times (c) 8 times (d) 2 times
35. 35.A cuboid is 9 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 588 sq cm (b) 147 sq cm (c) 294 sq cm (d) 270 sq cm
36. 36.A cuboid is 4 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 96 sq cm (b) 68 sq cm (c) 136 sq cm (d) 272 sq cm
37. 37.A cuboid is 12 cm long, 10 cm wide and 8 cm high. What is its volume? (a) 30 cu cm (b) 592 cu cm (c) 960 cu cm (d) 120 cu cm
38. 38.A cube has edges of 12 cm. What is its total surface area? (a) 1728 sq cm (b) 144 sq cm (c) 864 sq cm (d) 576 sq cm
39. 39.A cuboid is 6 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 162 cu cm (b) 18 cu cm (c) 126 cu cm (d) 16 cu cm
40. 40.A cuboid is 5 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 10 cu cm (b) 17 cu cm (c) 160 cu cm (d) 100 cu cm

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