Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 161 · 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 5 cm long, 4 cm wide and 4 cm high. What is its volume? (a) 13 cu cm (b) 112 cu cm (c) 20 cu cm (d) 80 cu cm
2. 2.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 88 sq cm (d) 2464 sq cm
3. 3.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 8 sq cm (c) 4 sq cm (d) 24 sq cm
4. 4.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 352 cm (d) 176 cm
5. 5.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
6. 6.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) 2 times (c) 4 times (d) 8 times
7. 7.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 2 times (c) 8 times (d) 4 times
8. 8.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
9. 9.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 132 cm (d) 1386 cm
10. 10.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
11. 11.A cube has edges of 6 cm. What is its volume? (a) 216 cu cm (b) 18 cu cm (c) 217 cu cm (d) 144 cu cm
12. 12.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
13. 13.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
14. 14.A cuboid is 12 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 66 sq cm (b) 72 sq cm (c) 132 sq cm (d) 264 sq cm
15. 15.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 5 times (d) 2 times
16. 16.A cube has edges of 11 cm. What is its total surface area? (a) 121 sq cm (b) 1331 sq cm (c) 484 sq cm (d) 726 sq cm
17. 17.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
18. 18.A cuboid is 6 cm long, 4 cm wide and 9 cm high. What is its volume? (a) 228 cu cm (b) 24 cu cm (c) 19 cu cm (d) 216 cu cm
19. 19.A cube has edges of 5 cm. What is its total surface area? (a) 150 sq cm (b) 25 sq cm (c) 125 sq cm (d) 100 sq cm
20. 20.A cube has edges of 8 cm. What is its total surface area? (a) 384 sq cm (b) 512 sq cm (c) 256 sq cm (d) 64 sq cm
21. 21.A cuboid is 7 cm long, 6 cm wide and 7 cm high. What is its total surface area? (a) 294 sq cm (b) 133 sq cm (c) 266 sq cm (d) 532 sq cm
22. 22.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 44 sq cm (d) 154 sq cm
23. 23.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
24. 24.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
25. 25.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 352 cm (d) 88 cm
26. 26.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm
27. 27.A cube has edges of 11 cm. What is its volume? (a) 33 cu cm (b) 726 cu cm (c) 484 cu cm (d) 1331 cu cm
28. 28.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 6 times (c) 9 times (d) 3 times
29. 29.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times
30. 30.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
31. 31.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 96 sq cm (c) 16 sq cm (d) 64 sq cm
32. 32.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 15 cu cm (b) 60 cu cm (c) 112 cu cm (d) 6 cu cm
33. 33.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 264 cm (d) 66 cm
34. 34.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
35. 35.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
36. 36.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
37. 37.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) 8 times (d) 64 times
38. 38.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 486 sq cm (c) 729 sq cm (d) 81 sq cm
39. 39.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
40. 40.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm

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