Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 776 · 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 3 cm high. What is its total surface area? (a) 124 sq cm (b) 31 sq cm (c) 30 sq cm (d) 62 sq cm
2. 2.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
3. 3.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 217 cu cm (c) 216 cu cm (d) 144 cu cm
4. 4.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
5. 5.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 125 times (c) 25 times (d) 10 times
6. 6.A cuboid is 10 cm long, 6 cm wide and 4 cm high. What is its volume? (a) 60 cu cm (b) 20 cu cm (c) 240 cu cm (d) 248 cu cm
7. 7.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
8. 8.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm
9. 9.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) 4 times (c) 5 times (d) 2 times
10. 10.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 352 cm (d) 2464 cm
11. 11.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 8 times (c) 64 times (d) 4 times
12. 12.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) 5 times (c) 4 times (d) 8 times
13. 13.A cuboid is 6 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 14 cu cm (b) 72 cu cm (c) 12 cu cm (d) 120 cu cm
14. 14.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 4 times (c) 8 times (d) 2 times
15. 15.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 176 cm (d) 88 cm
16. 16.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
17. 17.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) 9 times (c) 3 times (d) 6 times
18. 18.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 88 sq cm
19. 19.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
20. 20.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
21. 21.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 176 cm (d) 44 cm
22. 22.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
23. 23.A cuboid is 3 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 30 sq cm (b) 124 sq cm (c) 62 sq cm (d) 31 sq cm
24. 24.A cuboid is 5 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 52 sq cm (b) 60 sq cm (c) 104 sq cm (d) 208 sq cm
25. 25.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 21 sq cm (b) 18 sq cm (c) 42 sq cm (d) 84 sq cm
26. 26.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 384 cu cm (c) 256 cu cm (d) 24 cu cm
27. 27.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) 25 times (c) 5 times (d) 125 times
28. 28.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 3850 cm (d) 110 cm
29. 29.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 44 sq cm (d) 154 sq cm
30. 30.A cuboid is 9 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 90 sq cm (b) 146 sq cm (c) 292 sq cm (d) 73 sq cm
31. 31.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 16 times (c) 64 times (d) 8 times
32. 32.A cube has edges of 7 cm. What is its total surface area? (a) 49 sq cm (b) 196 sq cm (c) 343 sq cm (d) 294 sq cm
33. 33.A cube has edges of 10 cm. What is its volume? (a) 30 cu cm (b) 1000 cu cm (c) 600 cu cm (d) 400 cu cm
34. 34.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 6 times (c) 9 times (d) 27 times
35. 35.A cube has edges of 11 cm. What is its total surface area? (a) 121 sq cm (b) 1331 sq cm (c) 726 sq cm (d) 484 sq cm
36. 36.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
37. 37.A cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 400 sq cm (c) 100 sq cm (d) 1000 sq cm
38. 38.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 1232 sq cm
39. 39.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
40. 40.A cuboid is 11 cm long, 10 cm wide and 2 cm high. What is its volume? (a) 23 cu cm (b) 304 cu cm (c) 220 cu cm (d) 110 cu cm

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