Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 239 · 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 cube has edges of 10 cm. What is its total surface area? (a) 400 sq cm (b) 1000 sq cm (c) 100 sq cm (d) 600 sq cm
2. 2.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 sq cm
3. 3.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
4. 4.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
5. 5.If the radius of a circle 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
6. 6.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
7. 7.A cuboid is 10 cm long, 4 cm wide and 10 cm high. What is its volume? (a) 40 cu cm (b) 400 cu cm (c) 360 cu cm (d) 24 cu cm
8. 8.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
9. 9.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 6 times (c) 3 times (d) 27 times
10. 10.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 7 cu cm (b) 12 cu cm (c) 32 cu cm (d) 6 cu cm
11. 11.A cube has edges of 8 cm. What is its total surface area? (a) 256 sq cm (b) 512 sq cm (c) 384 sq cm (d) 64 sq cm
12. 12.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
13. 13.A cube has edges of 4 cm. What is its volume? (a) 64 cu cm (b) 12 cu cm (c) 65 cu cm (d) 96 cu cm
14. 14.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 97 sq cm (c) 96 sq cm (d) 64 sq cm
15. 15.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 2 times (d) 5 times
16. 16.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
17. 17.A cube has edges of 11 cm. What is its total surface area? (a) 726 sq cm (b) 484 sq cm (c) 1331 sq cm (d) 121 sq cm
18. 18.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
19. 19.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 216 sq cm (c) 217 sq cm (d) 36 sq cm
20. 20.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 64 times (c) 16 times (d) 4 times
21. 21.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 864 cu cm (c) 1728 cu cm (d) 36 cu cm
22. 22.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
23. 23.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 4 times (c) 8 times (d) 16 times
24. 24.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 616 sq cm (d) 44 sq cm
25. 25.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 256 cu cm (c) 24 cu cm (d) 384 cu cm
26. 26.A cuboid is 8 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 288 sq cm (b) 140 sq cm (c) 560 sq cm (d) 280 sq cm
27. 27.A cube has edges of 3 cm. What is its total surface area? (a) 54 sq cm (b) 36 sq cm (c) 27 sq cm (d) 9 sq cm
28. 28.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 6 cu cm (b) 92 cu cm (c) 13 cu cm (d) 48 cu cm
29. 29.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
30. 30.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) 25 times (d) 10 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) 10 times (d) 25 times
32. 32.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
33. 33.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 125 sq cm (c) 100 sq cm (d) 150 sq cm
34. 34.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 616 sq cm
35. 35.A cuboid is 11 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 262 cu cm (b) 33 cu cm (c) 231 cu cm (d) 21 cu cm
36. 36.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
37. 37.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 220 cm (d) 3850 cm
38. 38.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 16 times (d) 8 times
39. 39.A cuboid is 10 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 242 cu cm (b) 210 cu cm (c) 20 cu cm (d) 30 cu cm
40. 40.A cuboid is 4 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 136 sq cm (b) 96 sq cm (c) 68 sq cm (d) 272 sq cm

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