Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 190 · 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 cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 100 cu cm (c) 125 cu cm (d) 150 cu cm
2. 2.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 616 sq cm (d) 44 sq cm
3. 3.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
4. 4.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
5. 5.A cuboid is 8 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 448 sq cm (b) 224 sq cm (c) 112 sq cm (d) 192 sq cm
6. 6.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
7. 7.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
8. 8.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 512 cu cm (c) 384 cu cm (d) 256 cu cm
9. 9.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
10. 10.A cuboid is 11 cm long, 4 cm wide and 3 cm high. What is its total surface area? (a) 132 sq cm (b) 89 sq cm (c) 356 sq cm (d) 178 sq cm
11. 11.A cuboid is 6 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 11 cu cm (b) 18 cu cm (c) 36 cu cm (d) 72 cu cm
12. 12.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 5 times (c) 10 times (d) 125 times
13. 13.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 5 times (c) 4 times (d) 2 times
14. 14.A cuboid is 4 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 44 sq cm (b) 176 sq cm (c) 48 sq cm (d) 88 sq cm
15. 15.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
16. 16.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
17. 17.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) 16 times (d) 4 times
18. 18.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
19. 19.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 5 times (c) 25 times (d) 125 times
20. 20.A cuboid is 10 cm long, 9 cm wide and 5 cm high. What is its total surface area? (a) 740 sq cm (b) 370 sq cm (c) 450 sq cm (d) 185 sq cm
21. 21.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) 27 times (c) 3 times (d) 9 times
22. 22.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 8 times (c) 5 times (d) 4 times
23. 23.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 1728 sq cm (c) 144 sq cm (d) 576 sq cm
24. 24.A cuboid is 5 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 11 cu cm (b) 76 cu cm (c) 40 cu cm (d) 20 cu cm
25. 25.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 693 sq cm
26. 26.A cuboid is 8 cm long, 7 cm wide and 7 cm high. What is its total surface area? (a) 161 sq cm (b) 322 sq cm (c) 644 sq cm (d) 392 sq cm
27. 27.A cube has edges of 11 cm. What is its total surface area? (a) 121 sq cm (b) 484 sq cm (c) 726 sq cm (d) 1331 sq cm
28. 28.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 27 sq cm (c) 36 sq cm (d) 54 sq cm
29. 29.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
30. 30.A cuboid is 6 cm long, 4 cm wide and 5 cm high. What is its total surface area? (a) 296 sq cm (b) 148 sq cm (c) 74 sq cm (d) 120 sq cm
31. 31.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) 8 times (d) 4 times
32. 32.If the side of a square 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
33. 33.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 352 cm (d) 176 cm
34. 34.A cuboid is 12 cm long, 10 cm wide and 5 cm high. What is its volume? (a) 27 cu cm (b) 600 cu cm (c) 120 cu cm (d) 460 cu cm
35. 35.A cuboid is 10 cm long, 9 cm wide and 2 cm high. What is its total surface area? (a) 180 sq cm (b) 512 sq cm (c) 256 sq cm (d) 128 sq cm
36. 36.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
37. 37.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
38. 38.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
39. 39.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
40. 40.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) 10 times (c) 25 times (d) 125 times

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