Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 948 · 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 area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
2. 2.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 44 cm (d) 616 cm
3. 3.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 24 cu cm (c) 512 cu cm (d) 384 cu cm
4. 4.A cuboid is 11 cm long, 9 cm wide and 6 cm high. What is its volume? (a) 99 cu cm (b) 594 cu cm (c) 26 cu cm (d) 438 cu cm
5. 5.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) 4 times (c) 8 times (d) 16 times
6. 6.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
7. 7.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 352 cm (d) 88 cm
8. 8.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
9. 9.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 44 sq cm (d) 616 sq cm
10. 10.If the radius of a circle 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
11. 11.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 6 times (c) 27 times (d) 3 times
12. 12.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 2 times (c) 5 times (d) 8 times
13. 13.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) 5 times (d) 25 times
14. 14.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) 8 times (d) 5 times
15. 15.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
16. 16.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
17. 17.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
18. 18.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
19. 19.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
20. 20.A cuboid is 5 cm long, 4 cm wide and 8 cm high. What is its volume? (a) 184 cu cm (b) 20 cu cm (c) 17 cu cm (d) 160 cu cm
21. 21.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
22. 22.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) 2 times (c) 8 times (d) 6 times
23. 23.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 343 sq cm (c) 294 sq cm (d) 49 sq cm
24. 24.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 64 times (c) 4 times (d) 8 times
25. 25.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) 8 times (d) 4 times
26. 26.A cuboid is 4 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 24 sq cm (b) 52 sq cm (c) 26 sq cm (d) 104 sq cm
27. 27.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) 5 times (c) 25 times (d) 10 times
28. 28.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
29. 29.A cuboid is 6 cm long, 5 cm wide and 4 cm high. What is its volume? (a) 30 cu cm (b) 148 cu cm (c) 120 cu cm (d) 15 cu cm
30. 30.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 36 sq cm (c) 9 sq cm (d) 54 sq cm
31. 31.A cuboid is 12 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 432 sq cm (b) 768 sq cm (c) 384 sq cm (d) 192 sq cm
32. 32.A cube has edges of 11 cm. What is its total surface area? (a) 121 sq cm (b) 726 sq cm (c) 484 sq cm (d) 1331 sq cm
33. 33.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
34. 34.A cuboid is 8 cm long, 7 cm wide and 10 cm high. What is its volume? (a) 412 cu cm (b) 560 cu cm (c) 56 cu cm (d) 25 cu cm
35. 35.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) 16 times (c) 4 times (d) 8 times
36. 36.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 24 cu cm (c) 6 cu cm (d) 16 cu cm
37. 37.A cuboid is 4 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 100 sq cm (b) 50 sq cm (c) 56 sq cm (d) 200 sq cm
38. 38.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 132 sq cm (d) 5544 sq cm
39. 39.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 66 cm (d) 264 cm
40. 40.A cube has edges of 4 cm. What is its volume? (a) 64 cu cm (b) 96 cu cm (c) 65 cu cm (d) 12 cu cm

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