Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 308 · 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 8 cm. What is its total surface area? (a) 384 sq cm (b) 64 sq cm (c) 256 sq cm (d) 512 sq cm
2. 2.A cuboid is 4 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 48 cu cm (b) 12 cu cm (c) 80 cu cm (d) 11 cu cm
3. 3.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
4. 4.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 1386 cm (d) 66 cm
5. 5.A cuboid is 12 cm long, 10 cm wide and 6 cm high. What is its total surface area? (a) 1008 sq cm (b) 720 sq cm (c) 252 sq cm (d) 504 sq cm
6. 6.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) 10 times (d) 25 times
7. 7.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
8. 8.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 65 sq cm (b) 128 sq cm (c) 32 sq cm (d) 64 sq cm
9. 9.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
10. 10.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 486 sq cm (c) 324 sq cm (d) 729 sq cm
11. 11.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 3 times (c) 9 times (d) 6 times
12. 12.A cuboid is 10 cm long, 9 cm wide and 8 cm high. What is its total surface area? (a) 720 sq cm (b) 968 sq cm (c) 242 sq cm (d) 484 sq cm
13. 13.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 384 cu cm (c) 512 cu cm (d) 256 cu cm
14. 14.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
15. 15.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
16. 16.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
17. 17.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm
18. 18.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
19. 19.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
20. 20.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
21. 21.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) 64 times (c) 16 times (d) 4 times
22. 22.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 64 cu cm (c) 65 cu cm (d) 12 cu 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) 16 times (b) 4 times (c) 64 times (d) 8 times
24. 24.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
25. 25.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) 3 times (c) 9 times (d) 6 times
26. 26.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
27. 27.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
28. 28.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
29. 29.A cuboid is 11 cm long, 5 cm wide and 3 cm high. What is its volume? (a) 19 cu cm (b) 55 cu cm (c) 165 cu cm (d) 206 cu cm
30. 30.A cuboid is 7 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 41 sq cm (b) 82 sq cm (c) 42 sq cm (d) 164 sq cm
31. 31.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) 8 times (c) 5 times (d) 4 times
32. 32.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 144 cu cm (c) 18 cu cm (d) 216 cu cm
33. 33.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 125 times (c) 10 times (d) 5 times
34. 34.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 6 cu cm (b) 42 cu cm (c) 18 cu cm (d) 8 cu cm
35. 35.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 21 cu cm (c) 343 cu cm (d) 196 cu cm
36. 36.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) 27 times (c) 6 times (d) 9 times
37. 37.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
38. 38.A cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 100 sq cm (c) 1000 sq cm (d) 400 sq cm
39. 39.A cuboid is 8 cm long, 6 cm wide and 2 cm high. What is its total surface area? (a) 76 sq cm (b) 96 sq cm (c) 152 sq cm (d) 304 sq cm
40. 40.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 125 sq cm (c) 150 sq cm (d) 25 sq cm

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