Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 191 · 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 4 cm. What is its total surface area? (a) 64 sq cm (b) 16 sq cm (c) 97 sq cm (d) 96 sq cm
2. 2.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 24 cu cm (c) 256 cu cm (d) 512 cu cm
3. 3.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq cm
4. 4.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
5. 5.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
6. 6.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
7. 7.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 6 times (c) 3 times (d) 27 times
8. 8.A cuboid is 4 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 48 cu cm (b) 12 cu cm (c) 11 cu cm (d) 80 cu cm
9. 9.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 5544 sq cm
10. 10.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 10 times (c) 25 times (d) 5 times
11. 11.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
12. 12.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 308 sq cm
13. 13.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
14. 14.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) 64 times (c) 4 times (d) 8 times
15. 15.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) 4 times (c) 64 times (d) 16 times
16. 16.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 4 times (c) 2 times (d) 8 times
17. 17.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 44 sq cm (d) 77 sq cm
18. 18.A cuboid is 4 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 56 sq cm (b) 112 sq cm (c) 64 sq cm (d) 224 sq cm
19. 19.A cuboid is 7 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 105 cu cm (b) 15 cu cm (c) 21 cu cm (d) 142 cu cm
20. 20.A cuboid is 12 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 544 sq cm (b) 136 sq cm (c) 272 sq cm (d) 192 sq cm
21. 21.A cuboid is 7 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 50 sq cm (b) 200 sq cm (c) 100 sq cm (d) 56 sq cm
22. 22.If the side of a square 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
23. 23.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 30 cu cm (c) 600 cu cm (d) 400 cu cm
24. 24.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
25. 25.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 54 cu cm (c) 9 cu cm (d) 36 cu cm
26. 26.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
27. 27.A cuboid is 5 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 40 sq cm (b) 152 sq cm (c) 76 sq cm (d) 38 sq cm
28. 28.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
29. 29.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
30. 30.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 32 cu cm (b) 6 cu cm (c) 7 cu cm (d) 12 cu cm
31. 31.A cuboid is 10 cm long, 6 cm wide and 7 cm high. What is its volume? (a) 23 cu cm (b) 60 cu cm (c) 420 cu cm (d) 344 cu cm
32. 32.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 2464 cm (d) 352 cm
33. 33.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) 6 times (c) 9 times (d) 3 times
34. 34.A cuboid is 7 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 18 cu cm (b) 21 cu cm (c) 202 cu cm (d) 168 cu cm
35. 35.A cuboid is 11 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 139 sq cm (b) 198 sq cm (c) 556 sq cm (d) 278 sq cm
36. 36.If the radius of a circle 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
37. 37.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
38. 38.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 88 cm (d) 44 cm
39. 39.A cuboid is 6 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 188 cu cm (b) 168 cu cm (c) 24 cu cm (d) 17 cu cm
40. 40.A cuboid is 10 cm long, 6 cm wide and 8 cm high. What is its volume? (a) 60 cu cm (b) 24 cu cm (c) 480 cu cm (d) 376 cu cm

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