Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 217 · 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 diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
2. 2.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 176 sq cm
3. 3.A cube has edges of 4 cm. What is its total surface area? (a) 96 sq cm (b) 16 sq cm (c) 64 sq cm (d) 97 sq cm
4. 4.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 176 cm (d) 616 cm
5. 5.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 88 cm (d) 176 cm
6. 6.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 9 times (c) 6 times (d) 3 times
7. 7.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) 27 times (c) 9 times (d) 3 times
8. 8.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
9. 9.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
10. 10.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 102 cu cm (b) 14 cu cm (c) 54 cu cm (d) 6 cu cm
11. 11.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
12. 12.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 4 sq cm (c) 24 sq cm (d) 16 sq cm
13. 13.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
14. 14.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 10 times (c) 25 times (d) 5 times
15. 15.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) 16 times (c) 64 times (d) 4 times
16. 16.A cuboid is 7 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 95 sq cm (b) 126 sq cm (c) 380 sq cm (d) 190 sq cm
17. 17.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
18. 18.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
19. 19.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) 2 times (c) 4 times (d) 5 times
20. 20.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
21. 21.A cuboid is 5 cm long, 4 cm wide and 5 cm high. What is its total surface area? (a) 260 sq cm (b) 100 sq cm (c) 65 sq cm (d) 130 sq cm
22. 22.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
23. 23.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 2464 cm (d) 352 cm
24. 24.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 150 cu cm (c) 100 cu cm (d) 125 cu cm
25. 25.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 4 times (c) 2 times (d) 8 times
26. 26.A cuboid is 11 cm long, 9 cm wide and 2 cm high. What is its total surface area? (a) 139 sq cm (b) 198 sq cm (c) 278 sq cm (d) 556 sq cm
27. 27.A cuboid is 10 cm long, 4 cm wide and 4 cm high. What is its volume? (a) 40 cu cm (b) 18 cu cm (c) 160 cu cm (d) 192 cu cm
28. 28.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 400 cu cm (c) 30 cu cm (d) 1000 cu cm
29. 29.A cuboid is 9 cm long, 8 cm wide and 6 cm high. What is its volume? (a) 72 cu cm (b) 23 cu cm (c) 348 cu cm (d) 432 cu cm
30. 30.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) 25 times (c) 125 times (d) 5 times
31. 31.A cuboid is 10 cm long, 6 cm wide and 7 cm high. What is its total surface area? (a) 344 sq cm (b) 688 sq cm (c) 172 sq cm (d) 420 sq cm
32. 32.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
33. 33.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
34. 34.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 42 sq cm (b) 164 sq cm (c) 41 sq cm (d) 82 sq cm
35. 35.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 42 sq cm (b) 18 sq cm (c) 84 sq cm (d) 21 sq cm
36. 36.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
37. 37.A cuboid is 11 cm long, 5 cm wide and 3 cm high. What is its total surface area? (a) 103 sq cm (b) 165 sq cm (c) 412 sq cm (d) 206 sq cm
38. 38.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 6 cu cm (c) 8 cu cm (d) 24 cu cm
39. 39.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
40. 40.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 66 cm (d) 264 cm

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