Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 503 · 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 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 88 cm (d) 44 cm
2. 2.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
3. 3.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 42 sq cm (b) 82 sq cm (c) 41 sq cm (d) 164 sq cm
4. 4.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 88 cm (d) 2464 cm
5. 5.A cuboid is 10 cm long, 4 cm wide and 5 cm high. What is its total surface area? (a) 200 sq cm (b) 220 sq cm (c) 440 sq cm (d) 110 sq cm
6. 6.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 81 sq cm (c) 486 sq cm (d) 729 sq cm
7. 7.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
8. 8.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 125 cu cm (c) 15 cu cm (d) 100 cu cm
9. 9.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
10. 10.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
11. 11.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
12. 12.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) 6 times (c) 27 times (d) 9 times
13. 13.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) 4 times (c) 2 times (d) 6 times
14. 14.A cube has edges of 6 cm. What is its volume? (a) 216 cu cm (b) 18 cu cm (c) 144 cu cm (d) 217 cu cm
15. 15.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
16. 16.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 1232 sq cm
17. 17.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
18. 18.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
19. 19.A cuboid is 6 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 180 sq cm (b) 144 sq cm (c) 360 sq cm (d) 90 sq cm
20. 20.A cuboid is 11 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 304 sq cm (b) 152 sq cm (c) 220 sq cm (d) 608 sq cm
21. 21.A cuboid is 6 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 104 cu cm (b) 60 cu cm (c) 12 cu cm (d) 13 cu cm
22. 22.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 44 sq cm (d) 616 sq cm
23. 23.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 10 times (c) 25 times (d) 125 times
24. 24.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 3 times (c) 6 times (d) 27 times
25. 25.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 12 cu cm (c) 64 cu cm (d) 65 cu cm
26. 26.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 24 cu cm (c) 6 cu cm (d) 16 cu cm
27. 27.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 352 cm (d) 88 cm
28. 28.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 176 cm (d) 88 cm
29. 29.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 22 cm (d) 154 cm
30. 30.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
31. 31.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
32. 32.A cuboid is 10 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 20 cu cm (b) 18 cu cm (c) 120 cu cm (d) 184 cu cm
33. 33.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 25 times (c) 5 times (d) 125 times
34. 34.A cuboid is 10 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 588 sq cm (b) 294 sq cm (c) 147 sq cm (d) 270 sq cm
35. 35.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
36. 36.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 97 sq cm (c) 16 sq cm (d) 96 sq cm
37. 37.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) 5 times (c) 8 times (d) 4 times
38. 38.A cube has edges of 2 cm. What is its total surface area? (a) 24 sq cm (b) 8 sq cm (c) 16 sq cm (d) 4 sq cm
39. 39.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 729 cu cm (c) 486 cu cm (d) 324 cu cm
40. 40.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 2 times (d) 5 times

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