Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 817 · 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 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
2. 2.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 256 sq cm (c) 384 sq cm (d) 512 sq cm
3. 3.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 9 times (c) 3 times (d) 27 times
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) 8 times (c) 4 times (d) 5 times
5. 5.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
6. 6.A cube has edges of 9 cm. What is its volume? (a) 729 cu cm (b) 27 cu cm (c) 324 cu cm (d) 486 cu cm
7. 7.A cuboid is 9 cm long, 4 cm wide and 4 cm high. What is its volume? (a) 176 cu cm (b) 144 cu cm (c) 36 cu cm (d) 17 cu cm
8. 8.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 176 sq cm
9. 9.A cube has edges of 10 cm. What is its volume? (a) 400 cu cm (b) 600 cu cm (c) 30 cu cm (d) 1000 cu cm
10. 10.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
11. 11.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
12. 12.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) 6 times (d) 9 times
13. 13.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) 3 times (c) 9 times (d) 6 times
14. 14.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) 27 times (c) 9 times (d) 6 times
15. 15.A cube has edges of 9 cm. What is its total surface area? (a) 486 sq cm (b) 729 sq cm (c) 81 sq cm (d) 324 sq cm
16. 16.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 8 times (c) 4 times (d) 16 times
17. 17.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
18. 18.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
19. 19.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
20. 20.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) 5 times (c) 8 times (d) 2 times
21. 21.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 41 sq cm (b) 82 sq cm (c) 42 sq cm (d) 164 sq cm
22. 22.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
23. 23.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
24. 24.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) 5 times (c) 10 times (d) 25 times
25. 25.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
26. 26.A cuboid is 7 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 28 sq cm (b) 32 sq cm (c) 128 sq cm (d) 64 sq cm
27. 27.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 2 times (c) 6 times (d) 4 times
28. 28.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 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) 8 times (b) 64 times (c) 4 times (d) 16 times
30. 30.A cuboid is 10 cm long, 5 cm wide and 7 cm high. What is its volume? (a) 50 cu cm (b) 22 cu cm (c) 350 cu cm (d) 310 cu cm
31. 31.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 132 cm (d) 264 cm
32. 32.A cube has edges of 7 cm. What is its total surface area? (a) 294 sq cm (b) 49 sq cm (c) 343 sq cm (d) 196 sq cm
33. 33.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 88 cm (d) 154 cm
34. 34.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 384 cu cm (c) 512 cu cm (d) 256 cu cm
35. 35.A cuboid is 8 cm long, 7 cm wide and 8 cm high. What is its total surface area? (a) 176 sq cm (b) 352 sq cm (c) 448 sq cm (d) 704 sq cm
36. 36.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
37. 37.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 8 cu cm (b) 17 cu cm (c) 40 cu cm (d) 16 cu cm
38. 38.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) 5 times (c) 10 times (d) 125 times
39. 39.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
40. 40.A cuboid is 12 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 150 sq cm (b) 216 sq cm (c) 300 sq cm (d) 600 sq cm

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