Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 977 · 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 5 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 90 cu cm (b) 10 cu cm (c) 50 cu cm (d) 12 cu cm
2. 2.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 216 sq cm (c) 36 sq cm (d) 217 sq cm
3. 3.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 1232 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.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 88 cm (d) 176 cm
6. 6.A cuboid is 5 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 78 cu cm (b) 11 cu cm (c) 45 cu cm (d) 15 cu cm
7. 7.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) 10 times (c) 25 times (d) 5 times
8. 8.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
9. 9.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) 4 times (c) 2 times (d) 8 times
10. 10.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 3 times (c) 27 times (d) 9 times
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) 2464 sq cm (d) 308 sq cm
12. 12.A cube has edges of 2 cm. What is its total surface area? (a) 4 sq cm (b) 8 sq cm (c) 16 sq cm (d) 24 sq cm
13. 13.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 15 cu cm (c) 100 cu cm (d) 125 cu cm
14. 14.A cuboid is 5 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 90 cu cm (b) 126 cu cm (c) 15 cu cm (d) 14 cu cm
15. 15.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
16. 16.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 125 times (c) 25 times (d) 10 times
17. 17.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 54 cu cm (c) 36 cu cm (d) 27 cu cm
18. 18.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
19. 19.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
20. 20.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
21. 21.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 9856 sq cm
22. 22.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) 5 times (c) 8 times (d) 2 times
23. 23.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 42 cu cm (b) 6 cu cm (c) 12 cu cm (d) 82 cu cm
24. 24.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
25. 25.A cuboid is 6 cm long, 5 cm wide and 2 cm high. What is its total surface area? (a) 60 sq cm (b) 104 sq cm (c) 208 sq cm (d) 52 sq cm
26. 26.A cube has edges of 11 cm. What is its volume? (a) 726 cu cm (b) 1331 cu cm (c) 33 cu cm (d) 484 cu cm
27. 27.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 512 sq cm (c) 384 sq cm (d) 256 sq cm
28. 28.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 16 times (c) 8 times (d) 64 times
29. 29.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
30. 30.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) 8 times (d) 4 times
31. 31.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
32. 32.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) 6 times (d) 4 times
33. 33.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
34. 34.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
35. 35.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 77 sq cm (d) 44 sq cm
36. 36.A cuboid is 6 cm long, 3 cm wide and 10 cm high. What is its volume? (a) 216 cu cm (b) 18 cu cm (c) 19 cu cm (d) 180 cu cm
37. 37.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 24 cu cm (c) 16 cu cm (d) 8 cu cm
38. 38.A cube has edges of 6 cm. What is its volume? (a) 216 cu cm (b) 217 cu cm (c) 18 cu cm (d) 144 cu cm
39. 39.A cuboid is 5 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 50 sq cm (b) 180 sq cm (c) 45 sq cm (d) 90 sq cm
40. 40.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) 4 times (c) 64 times (d) 8 times

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