Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 656 · 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.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 40 cu cm (b) 8 cu cm (c) 16 cu cm (d) 17 cu cm
2. 2.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 54 sq cm (c) 27 sq cm (d) 36 sq cm
3. 3.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
4. 4.A cuboid is 8 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 360 sq cm (b) 90 sq cm (c) 144 sq cm (d) 180 sq cm
5. 5.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
6. 6.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 64 times (c) 4 times (d) 16 times
7. 7.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 15 cu cm (b) 6 cu cm (c) 112 cu cm (d) 60 cu cm
8. 8.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 384 sq cm (c) 256 sq cm (d) 64 sq cm
9. 9.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 6 times (c) 4 times (d) 8 times
10. 10.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
11. 11.A cuboid is 11 cm long, 6 cm wide and 8 cm high. What is its total surface area? (a) 528 sq cm (b) 404 sq cm (c) 202 sq cm (d) 808 sq cm
12. 12.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
13. 13.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
14. 14.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 324 sq cm (c) 81 sq cm (d) 486 sq cm
15. 15.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
16. 16.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
17. 17.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 176 cm (d) 44 cm
18. 18.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) 4 times (c) 8 times (d) 5 times
19. 19.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
20. 20.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 44 sq cm (d) 616 sq cm
21. 21.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 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.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 96 sq cm (c) 97 sq cm (d) 64 sq cm
24. 24.A cube has edges of 11 cm. What is its total surface area? (a) 726 sq cm (b) 121 sq cm (c) 1331 sq cm (d) 484 sq cm
25. 25.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 8 times (c) 2 times (d) 4 times
26. 26.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
27. 27.A cuboid is 5 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 38 sq cm (b) 76 sq cm (c) 40 sq cm (d) 152 sq cm
28. 28.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
29. 29.A cuboid is 9 cm long, 7 cm wide and 4 cm high. What is its total surface area? (a) 252 sq cm (b) 127 sq cm (c) 508 sq cm (d) 254 sq cm
30. 30.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
31. 31.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 25 times (d) 10 times
32. 32.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 18 cu cm (c) 216 cu cm (d) 144 cu cm
33. 33.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) 27 times (c) 9 times (d) 6 times
34. 34.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 18 sq cm (b) 42 sq cm (c) 84 sq cm (d) 21 sq cm
35. 35.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 4 times (c) 8 times (d) 64 times
36. 36.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 125 times (c) 25 times (d) 5 times
37. 37.A cuboid is 11 cm long, 9 cm wide and 10 cm high. What is its volume? (a) 99 cu cm (b) 598 cu cm (c) 990 cu cm (d) 30 cu cm
38. 38.A cuboid is 8 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 22 cu cm (b) 32 cu cm (c) 320 cu cm (d) 304 cu cm
39. 39.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 88 cm (d) 352 cm
40. 40.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 308 sq cm (d) 2464 sq cm

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