Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 421 · 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 3 times as long, how many times as big does its area become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
2. 2.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
3. 3.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 49 sq cm (c) 294 sq cm (d) 343 sq cm
4. 4.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 3850 cm (d) 440 cm
5. 5.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
6. 6.A cube has edges of 9 cm. What is its volume? (a) 486 cu cm (b) 324 cu cm (c) 729 cu cm (d) 27 cu cm
7. 7.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm
8. 8.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) 16 times (d) 8 times
9. 9.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
10. 10.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 512 cu cm (c) 384 cu cm (d) 256 cu cm
11. 11.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
12. 12.A cube has edges of 6 cm. What is its volume? (a) 216 cu cm (b) 18 cu cm (c) 144 cu cm (d) 217 cu cm
13. 13.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
14. 14.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
15. 15.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 9856 sq cm
16. 16.A cube has edges of 10 cm. What is its volume? (a) 30 cu cm (b) 400 cu cm (c) 600 cu cm (d) 1000 cu cm
17. 17.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 32 sq cm (b) 65 sq cm (c) 128 sq cm (d) 64 sq cm
18. 18.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 100 sq cm (c) 125 sq cm (d) 150 sq cm
19. 19.A cube has edges of 4 cm. What is its total surface area? (a) 96 sq cm (b) 64 sq cm (c) 97 sq cm (d) 16 sq cm
20. 20.A cube has edges of 10 cm. What is its total surface area? (a) 100 sq cm (b) 400 sq cm (c) 1000 sq cm (d) 600 sq cm
21. 21.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 110 cm (d) 440 cm
22. 22.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
23. 23.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 4 times (c) 5 times (d) 8 times
24. 24.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 264 cm (d) 1386 cm
25. 25.A cuboid is 8 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 76 sq cm (b) 304 sq cm (c) 152 sq cm (d) 96 sq cm
26. 26.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 2464 cm (d) 352 cm
27. 27.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 150 cu cm (c) 100 cu cm (d) 125 cu cm
28. 28.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
29. 29.A cuboid is 6 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 72 cu cm (b) 11 cu cm (c) 12 cu cm (d) 36 cu cm
30. 30.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
31. 31.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
32. 32.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) 8 times (d) 4 times
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) 5 times (b) 4 times (c) 8 times (d) 2 times
34. 34.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
35. 35.A cube has edges of 4 cm. What is its volume? (a) 64 cu cm (b) 65 cu cm (c) 12 cu cm (d) 96 cu cm
36. 36.A cuboid is 11 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 356 sq cm (b) 178 sq cm (c) 89 sq cm (d) 132 sq cm
37. 37.A cuboid is 11 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 636 sq cm (b) 318 sq cm (c) 297 sq cm (d) 159 sq cm
38. 38.A cuboid is 5 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 264 sq cm (b) 132 sq cm (c) 80 sq cm (d) 66 sq cm
39. 39.A cuboid is 5 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 62 cu cm (b) 30 cu cm (c) 10 cu cm (d) 15 cu cm
40. 40.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm

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