Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 121 · 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 9 cm. What is its total surface area? (a) 81 sq cm (b) 324 sq cm (c) 486 sq cm (d) 729 sq cm
2. 2.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
3. 3.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 2 times (c) 8 times (d) 5 times
4. 4.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 5 times (c) 125 times (d) 25 times
5. 5.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 3 times (c) 6 times (d) 27 times
6. 6.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
7. 7.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 4 times (d) 8 times
8. 8.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
9. 9.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 616 cm (d) 176 cm
10. 10.A cuboid is 12 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 180 sq cm (b) 111 sq cm (c) 444 sq cm (d) 222 sq cm
11. 11.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
12. 12.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 64 cu cm (c) 12 cu cm (d) 65 cu cm
13. 13.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 576 cu cm (c) 36 cu cm (d) 1728 cu cm
14. 14.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 110 cm (d) 440 cm
15. 15.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) 9 times (c) 3 times (d) 6 times
16. 16.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
17. 17.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
18. 18.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 132 sq cm (d) 5544 sq cm
19. 19.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 616 cm (d) 44 cm
20. 20.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
21. 21.A cuboid is 7 cm long, 6 cm wide and 5 cm high. What is its total surface area? (a) 210 sq cm (b) 214 sq cm (c) 107 sq cm (d) 428 sq cm
22. 22.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 110 cm (d) 440 cm
23. 23.A cuboid is 10 cm long, 6 cm wide and 6 cm high. What is its volume? (a) 312 cu cm (b) 360 cu cm (c) 22 cu cm (d) 60 cu cm
24. 24.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) 25 times (d) 10 times
25. 25.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 4 times (c) 64 times (d) 8 times
26. 26.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) 16 times (c) 8 times (d) 64 times
27. 27.A cuboid is 4 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 62 sq cm (b) 124 sq cm (c) 72 sq cm (d) 248 sq cm
28. 28.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
29. 29.A cube has edges of 6 cm. What is its volume? (a) 144 cu cm (b) 216 cu cm (c) 217 cu cm (d) 18 cu cm
30. 30.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) 3 times (c) 6 times (d) 27 times
31. 31.A cube has edges of 10 cm. What is its volume? (a) 400 cu cm (b) 1000 cu cm (c) 30 cu cm (d) 600 cu cm
32. 32.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 88 cm (d) 352 cm
33. 33.A cuboid is 10 cm long, 5 cm wide and 7 cm high. What is its volume? (a) 310 cu cm (b) 22 cu cm (c) 50 cu cm (d) 350 cu cm
34. 34.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) 8 times (c) 4 times (d) 6 times
35. 35.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 54 cu cm (c) 9 cu cm (d) 36 cu cm
36. 36.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 8 cu cm (c) 24 cu cm (d) 16 cu cm
37. 37.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
38. 38.A cuboid is 5 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 24 sq cm (b) 96 sq cm (c) 20 sq cm (d) 48 sq cm
39. 39.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 294 cu cm (c) 196 cu cm (d) 343 cu cm
40. 40.A cuboid is 5 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 76 cu cm (b) 11 cu cm (c) 40 cu cm (d) 20 cu cm

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