Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 248 · 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 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) 4 times (d) 8 times
2. 2.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 9 times (c) 3 times (d) 6 times
3. 3.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 308 sq cm
4. 4.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
5. 5.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
6. 6.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
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 cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 324 sq cm (c) 729 sq cm (d) 486 sq cm
9. 9.A cube has edges of 7 cm. What is its total surface area? (a) 294 sq cm (b) 343 sq cm (c) 49 sq cm (d) 196 sq cm
10. 10.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
11. 11.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 25 times (c) 10 times (d) 125 times
12. 12.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) 4 times (c) 8 times (d) 64 times
13. 13.A cube has edges of 2 cm. What is its total surface area? (a) 24 sq cm (b) 4 sq cm (c) 8 sq cm (d) 16 sq cm
14. 14.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 9 times (c) 6 times (d) 27 times
15. 15.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 36 cu cm (c) 576 cu cm (d) 1728 cu cm
16. 16.A cube has edges of 11 cm. What is its volume? (a) 726 cu cm (b) 1331 cu cm (c) 484 cu cm (d) 33 cu cm
17. 17.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
18. 18.A cuboid is 7 cm long, 5 cm wide and 7 cm high. What is its total surface area? (a) 245 sq cm (b) 476 sq cm (c) 119 sq cm (d) 238 sq cm
19. 19.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 176 cm (d) 88 cm
20. 20.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 6 cu cm (b) 112 cu cm (c) 15 cu cm (d) 60 cu cm
21. 21.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 88 cm (d) 154 cm
22. 22.If the radius of a circle 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
23. 23.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) 9 times (c) 6 times (d) 27 times
24. 24.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 308 sq cm
25. 25.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 693 sq cm
26. 26.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 3 times (c) 27 times (d) 6 times
27. 27.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
28. 28.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 121 sq cm (c) 484 sq cm (d) 726 sq cm
29. 29.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
30. 30.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 27 cu cm (c) 36 cu cm (d) 9 cu cm
31. 31.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 8 times (c) 16 times (d) 64 times
32. 32.A cuboid is 9 cm long, 5 cm wide and 4 cm high. What is its total surface area? (a) 101 sq cm (b) 180 sq cm (c) 404 sq cm (d) 202 sq cm
33. 33.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
34. 34.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 196 cu cm (c) 343 cu cm (d) 21 cu cm
35. 35.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 256 cu cm (c) 384 cu cm (d) 24 cu cm
36. 36.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 52 sq cm (b) 104 sq cm (c) 26 sq cm (d) 24 sq cm
37. 37.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 352 cm (d) 88 cm
38. 38.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) 25 times (c) 125 times (d) 10 times
39. 39.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 15 cu cm (c) 125 cu cm (d) 100 cu cm
40. 40.A cube has edges of 10 cm. What is its total surface area? (a) 100 sq cm (b) 600 sq cm (c) 400 sq cm (d) 1000 sq cm

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