Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 926 · 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 6 cm long, 4 cm wide and 9 cm high. What is its volume? (a) 24 cu cm (b) 19 cu cm (c) 228 cu cm (d) 216 cu cm
2. 2.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 4 times (c) 8 times (d) 2 times
3. 3.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 46 sq cm (b) 92 sq cm (c) 48 sq cm (d) 184 sq cm
4. 4.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 5 times (c) 8 times (d) 4 times
5. 5.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 616 sq cm
6. 6.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
7. 7.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
8. 8.A cuboid is 12 cm long, 10 cm wide and 2 cm high. What is its total surface area? (a) 656 sq cm (b) 164 sq cm (c) 328 sq cm (d) 240 sq cm
9. 9.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 12 cu cm (c) 65 cu cm (d) 64 cu cm
10. 10.A cube has edges of 9 cm. What is its volume? (a) 486 cu cm (b) 729 cu cm (c) 324 cu cm (d) 27 cu cm
11. 11.A cuboid is 9 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 72 cu cm (b) 15 cu cm (c) 124 cu cm (d) 36 cu cm
12. 12.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
13. 13.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) 25 times (c) 5 times (d) 10 times
14. 14.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
15. 15.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
16. 16.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 77 sq cm (d) 616 sq cm
17. 17.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 27 times (c) 6 times (d) 3 times
18. 18.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 66 cm (d) 1386 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) 132 cm (d) 66 cm
20. 20.A cuboid is 4 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 84 cu cm (b) 14 cu cm (c) 12 cu cm (d) 122 cu cm
21. 21.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 4 times (c) 16 times (d) 64 times
22. 22.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
23. 23.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) 5 times (c) 125 times (d) 25 times
24. 24.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 100 cu cm (c) 150 cu cm (d) 125 cu cm
25. 25.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
26. 26.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
27. 27.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) 6 times (c) 9 times (d) 27 times
28. 28.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) 5 times (c) 2 times (d) 8 times
29. 29.A cuboid is 7 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 102 cu cm (b) 21 cu cm (c) 63 cu cm (d) 13 cu cm
30. 30.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 1232 sq cm
31. 31.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 27 sq cm (c) 36 sq cm (d) 54 sq cm
32. 32.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
33. 33.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
34. 34.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
35. 35.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 8 cu cm (c) 16 cu cm (d) 6 cu cm
36. 36.A cuboid is 6 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 18 cu cm (b) 184 cu cm (c) 12 cu cm (d) 120 cu cm
37. 37.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 54 cu cm (c) 9 cu cm (d) 27 cu cm
38. 38.A cuboid is 8 cm long, 5 cm wide and 3 cm high. What is its total surface area? (a) 158 sq cm (b) 79 sq cm (c) 120 sq cm (d) 316 sq cm
39. 39.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
40. 40.A cube has edges of 7 cm. What is its total surface area? (a) 49 sq cm (b) 196 sq cm (c) 343 sq cm (d) 294 sq cm

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