Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 339 · 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.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) 16 times (c) 64 times (d) 8 times
2. 2.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 44 sq cm (d) 616 sq cm
3. 3.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
4. 4.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
5. 5.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 616 sq cm (d) 77 sq cm
6. 6.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
7. 7.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
8. 8.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
9. 9.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
10. 10.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
11. 11.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 220 cm (d) 440 cm
12. 12.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 36 cu cm (c) 54 cu cm (d) 27 cu cm
13. 13.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) 5 times (c) 10 times (d) 25 times
14. 14.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
15. 15.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) 5 times (d) 4 times
16. 16.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 196 cu cm (c) 343 cu cm (d) 294 cu cm
17. 17.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 5544 sq cm
18. 18.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
19. 19.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) 8 times (c) 64 times (d) 4 times
20. 20.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
21. 21.A cuboid is 10 cm long, 8 cm wide and 5 cm high. What is its volume? (a) 23 cu cm (b) 400 cu cm (c) 340 cu cm (d) 80 cu cm
22. 22.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 3850 cm (d) 440 cm
23. 23.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) 3 times (c) 9 times (d) 6 times
24. 24.A cube has edges of 9 cm. What is its volume? (a) 486 cu cm (b) 324 cu cm (c) 27 cu cm (d) 729 cu cm
25. 25.A cube has edges of 2 cm. What is its total surface area? (a) 4 sq cm (b) 16 sq cm (c) 8 sq cm (d) 24 sq cm
26. 26.A cuboid is 5 cm long, 4 cm wide and 3 cm high. What is its total surface area? (a) 94 sq cm (b) 47 sq cm (c) 60 sq cm (d) 188 sq cm
27. 27.A cuboid is 11 cm long, 4 cm wide and 4 cm high. What is its volume? (a) 19 cu cm (b) 208 cu cm (c) 44 cu cm (d) 176 cu cm
28. 28.A cube has edges of 5 cm. What is its volume? (a) 100 cu cm (b) 150 cu cm (c) 15 cu cm (d) 125 cu cm
29. 29.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 104 sq cm (b) 52 sq cm (c) 26 sq cm (d) 24 sq cm
30. 30.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) 6 times (c) 2 times (d) 4 times
31. 31.A cuboid is 5 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 80 sq cm (b) 66 sq cm (c) 132 sq cm (d) 264 sq cm
32. 32.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
33. 33.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
34. 34.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 1386 cm (d) 66 cm
35. 35.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 3 times (c) 6 times (d) 27 times
36. 36.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
37. 37.A cube has edges of 11 cm. What is its total surface area? (a) 121 sq cm (b) 484 sq cm (c) 1331 sq cm (d) 726 sq cm
38. 38.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 256 cu cm (c) 512 cu cm (d) 384 cu cm
39. 39.A cuboid is 8 cm long, 7 cm wide and 10 cm high. What is its volume? (a) 25 cu cm (b) 560 cu cm (c) 412 cu cm (d) 56 cu cm
40. 40.A cuboid is 8 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 92 cu cm (b) 24 cu cm (c) 48 cu cm (d) 13 cu cm

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