Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 720 · 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.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
2. 2.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times
3. 3.A cube has edges of 9 cm. What is its total surface area? (a) 486 sq cm (b) 81 sq cm (c) 324 sq cm (d) 729 sq cm
4. 4.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
5. 5.A cuboid is 4 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 132 sq cm (b) 33 sq cm (c) 66 sq cm (d) 36 sq cm
6. 6.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) 2 times (c) 8 times (d) 4 times
7. 7.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
8. 8.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) 4 times (c) 8 times (d) 5 times
9. 9.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 616 cm (d) 176 cm
10. 10.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
11. 11.A cube has edges of 8 cm. What is its total surface area? (a) 256 sq cm (b) 512 sq cm (c) 64 sq cm (d) 384 sq cm
12. 12.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 44 sq cm (d) 154 sq cm
13. 13.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 616 cm (d) 44 cm
14. 14.A cube has edges of 7 cm. What is its volume? (a) 343 cu cm (b) 294 cu cm (c) 21 cu cm (d) 196 cu cm
15. 15.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 4 sq cm (c) 24 sq cm (d) 8 sq cm
16. 16.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 84 sq cm (b) 42 sq cm (c) 18 sq cm (d) 21 sq cm
17. 17.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
18. 18.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
19. 19.A cuboid is 10 cm long, 9 cm wide and 10 cm high. What is its total surface area? (a) 1120 sq cm (b) 900 sq cm (c) 280 sq cm (d) 560 sq cm
20. 20.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
21. 21.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
22. 22.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
23. 23.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) 6 times (c) 9 times (d) 27 times
24. 24.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) 125 times (c) 25 times (d) 5 times
25. 25.A cuboid is 7 cm long, 6 cm wide and 7 cm high. What is its volume? (a) 294 cu cm (b) 20 cu cm (c) 266 cu cm (d) 42 cu cm
26. 26.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 440 cm (d) 110 cm
27. 27.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
28. 28.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 1232 sq cm
29. 29.If the side of a square 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
30. 30.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 125 sq cm (c) 25 sq cm (d) 150 sq cm
31. 31.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) 5 times (c) 125 times (d) 10 times
32. 32.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
33. 33.A cuboid is 5 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 60 cu cm (b) 15 cu cm (c) 94 cu cm (d) 12 cu cm
34. 34.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 110 cm (d) 3850 cm
35. 35.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times
36. 36.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 6 times (c) 2 times (d) 8 times
37. 37.A cuboid is 11 cm long, 5 cm wide and 9 cm high. What is its volume? (a) 495 cu cm (b) 25 cu cm (c) 55 cu cm (d) 398 cu cm
38. 38.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
39. 39.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 56 sq cm (b) 60 sq cm (c) 224 sq cm (d) 112 sq cm
40. 40.A cuboid is 8 cm long, 7 cm wide and 7 cm high. What is its total surface area? (a) 392 sq cm (b) 161 sq cm (c) 322 sq cm (d) 644 sq cm

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