Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 544 · 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 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
2. 2.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
3. 3.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
4. 4.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) 64 times (c) 8 times (d) 16 times
5. 5.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 4 times (c) 8 times (d) 16 times
6. 6.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
7. 7.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
8. 8.A cuboid is 9 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 246 sq cm (b) 123 sq cm (c) 216 sq cm (d) 492 sq cm
9. 9.A cube has edges of 11 cm. What is its total surface area? (a) 121 sq cm (b) 484 sq cm (c) 726 sq cm (d) 1331 sq cm
10. 10.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
11. 11.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) 125 times (c) 10 times (d) 25 times
12. 12.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 12 cu cm (c) 96 cu cm (d) 64 cu cm
13. 13.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 125 times (c) 5 times (d) 10 times
14. 14.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
15. 15.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 726 cu cm (c) 1331 cu cm (d) 33 cu cm
16. 16.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 2 times (c) 8 times (d) 6 times
17. 17.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 16 sq cm (c) 4 sq cm (d) 24 sq cm
18. 18.A cuboid is 8 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 24 cu cm (b) 180 cu cm (c) 144 cu cm (d) 17 cu cm
19. 19.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 4 times (b) 5 times (c) 8 times (d) 2 times
20. 20.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
21. 21.A cuboid is 12 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 144 sq cm (b) 192 sq cm (c) 96 sq cm (d) 384 sq cm
22. 22.A cuboid is 6 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 180 cu cm (b) 17 cu cm (c) 18 cu cm (d) 144 cu cm
23. 23.A cuboid is 7 cm long, 6 cm wide and 10 cm high. What is its total surface area? (a) 344 sq cm (b) 688 sq cm (c) 420 sq cm (d) 172 sq cm
24. 24.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 1386 cm (d) 264 cm
25. 25.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 176 cm (d) 616 cm
26. 26.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
27. 27.A cube has edges of 10 cm. What is its total surface area? (a) 100 sq cm (b) 600 sq cm (c) 1000 sq cm (d) 400 sq cm
28. 28.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
29. 29.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
30. 30.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 24 cu cm (c) 6 cu cm (d) 8 cu cm
31. 31.A cuboid is 11 cm long, 6 cm wide and 8 cm high. What is its volume? (a) 25 cu cm (b) 528 cu cm (c) 66 cu cm (d) 404 cu cm
32. 32.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq cm
33. 33.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
34. 34.A cuboid is 6 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 36 cu cm (b) 11 cu cm (c) 72 cu cm (d) 18 cu cm
35. 35.A cuboid is 10 cm long, 8 cm wide and 4 cm high. What is its total surface area? (a) 304 sq cm (b) 152 sq cm (c) 320 sq cm (d) 608 sq cm
36. 36.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 27 sq cm (c) 9 sq cm (d) 54 sq cm
37. 37.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 729 cu cm (c) 486 cu cm (d) 27 cu cm
38. 38.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
39. 39.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 352 cm (d) 88 cm
40. 40.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 30 cu cm (b) 10 cu cm (c) 62 cu cm (d) 6 cu cm

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