Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 287 · 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 9 cm long, 5 cm wide and 8 cm high. What is its total surface area? (a) 314 sq cm (b) 628 sq cm (c) 360 sq cm (d) 157 sq cm
2. 2.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
3. 3.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
4. 4.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 9 times (c) 6 times (d) 3 times
5. 5.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
6. 6.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
7. 7.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 486 sq cm (c) 729 sq cm (d) 324 sq cm
8. 8.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
9. 9.A cube has edges of 3 cm. What is its total surface area? (a) 54 sq cm (b) 27 sq cm (c) 36 sq cm (d) 9 sq cm
10. 10.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 40 cu cm (b) 16 cu cm (c) 17 cu cm (d) 8 cu cm
11. 11.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) 25 times (d) 10 times
12. 12.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 196 cu cm (c) 294 cu cm (d) 343 cu cm
13. 13.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) 8 times (c) 64 times (d) 16 times
14. 14.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 64 times (c) 8 times (d) 4 times
15. 15.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) 4 times (c) 16 times (d) 64 times
16. 16.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
17. 17.A cuboid is 10 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 360 sq cm (b) 400 sq cm (c) 180 sq cm (d) 720 sq cm
18. 18.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 216 cu cm (c) 18 cu cm (d) 144 cu cm
19. 19.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
20. 20.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 125 times (b) 25 times (c) 5 times (d) 10 times
21. 21.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
22. 22.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
23. 23.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
24. 24.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) 6 times (c) 27 times (d) 3 times
25. 25.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
26. 26.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
27. 27.A cuboid is 12 cm long, 4 cm wide and 8 cm high. What is its total surface area? (a) 352 sq cm (b) 176 sq cm (c) 704 sq cm (d) 384 sq cm
28. 28.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
29. 29.A cube has edges of 4 cm. What is its total surface area? (a) 96 sq cm (b) 64 sq cm (c) 97 sq cm (d) 16 sq cm
30. 30.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
31. 31.A cuboid is 5 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 104 cu cm (b) 60 cu cm (c) 13 cu cm (d) 10 cu cm
32. 32.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 25 times (b) 125 times (c) 5 times (d) 10 times
33. 33.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 616 sq cm
34. 34.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) 8 times (c) 2 times (d) 4 times
35. 35.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 36 cu cm (c) 27 cu cm (d) 9 cu 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) 5 times (b) 8 times (c) 2 times (d) 4 times
37. 37.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
38. 38.A cube has edges of 12 cm. What is its total surface area? (a) 144 sq cm (b) 864 sq cm (c) 576 sq cm (d) 1728 sq cm
39. 39.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 88 cm (d) 352 cm
40. 40.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 1728 cu cm (c) 576 cu cm (d) 36 cu cm

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