Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 411 · 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 volume? (a) 24 cu cm (b) 256 cu cm (c) 384 cu cm (d) 512 cu cm
2. 2.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) 9 times (c) 27 times (d) 3 times
3. 3.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
4. 4.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 54 cu cm (c) 36 cu cm (d) 9 cu cm
5. 5.A cube has edges of 11 cm. What is its volume? (a) 726 cu cm (b) 484 cu cm (c) 33 cu cm (d) 1331 cu cm
6. 6.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) 8 times (d) 16 times
7. 7.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 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) 64 times (b) 16 times (c) 4 times (d) 8 times
9. 9.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
10. 10.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 4 sq cm (c) 16 sq cm (d) 24 sq cm
11. 11.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 400 cu cm (c) 30 cu cm (d) 1000 cu cm
12. 12.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
13. 13.A cuboid is 10 cm long, 4 cm wide and 3 cm high. What is its total surface area? (a) 164 sq cm (b) 328 sq cm (c) 82 sq cm (d) 120 sq cm
14. 14.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
15. 15.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
16. 16.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
17. 17.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 8 times (c) 2 times (d) 4 times
18. 18.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 100 sq cm (c) 150 sq cm (d) 125 sq cm
19. 19.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 16 cu cm (c) 24 cu cm (d) 6 cu cm
20. 20.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
21. 21.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
22. 22.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
23. 23.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
24. 24.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
25. 25.A cube has edges of 12 cm. What is its total surface area? (a) 1728 sq cm (b) 576 sq cm (c) 144 sq cm (d) 864 sq cm
26. 26.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 125 times (c) 10 times (d) 5 times
27. 27.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 5 times (c) 10 times (d) 125 times
28. 28.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
29. 29.A cuboid is 12 cm long, 10 cm wide and 10 cm high. What is its total surface area? (a) 340 sq cm (b) 1360 sq cm (c) 680 sq cm (d) 1200 sq cm
30. 30.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 3850 cm (d) 110 cm
31. 31.A cuboid is 5 cm long, 4 cm wide and 7 cm high. What is its total surface area? (a) 83 sq cm (b) 140 sq cm (c) 166 sq cm (d) 332 sq cm
32. 32.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
33. 33.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 294 cu cm (c) 21 cu cm (d) 343 cu cm
34. 34.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 176 cm (d) 88 cm
35. 35.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
36. 36.If the side of a square 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
37. 37.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq cm
38. 38.A cuboid is 7 cm long, 6 cm wide and 3 cm high. What is its total surface area? (a) 324 sq cm (b) 126 sq cm (c) 162 sq cm (d) 81 sq cm
39. 39.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 216 cu cm (c) 144 cu cm (d) 18 cu cm
40. 40.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 65 cu cm (c) 12 cu cm (d) 64 cu cm

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