Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 471 · 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 3 cm. What is its volume? (a) 9 cu cm (b) 36 cu cm (c) 54 cu cm (d) 27 cu cm
2. 2.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 264 cm (d) 66 cm
3. 3.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
4. 4.A cuboid is 6 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 72 cu cm (b) 12 cu cm (c) 11 cu cm (d) 36 cu cm
5. 5.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 6 times (c) 3 times (d) 9 times
6. 6.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 16 times (c) 64 times (d) 4 times
7. 7.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
8. 8.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
9. 9.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 64 sq cm (c) 256 sq cm (d) 384 sq cm
10. 10.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
11. 11.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
12. 12.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) 8 times (d) 2 times
13. 13.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
14. 14.A cuboid is 8 cm long, 6 cm wide and 9 cm high. What is its volume? (a) 348 cu cm (b) 432 cu cm (c) 23 cu cm (d) 48 cu cm
15. 15.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) 5 times (c) 4 times (d) 8 times
16. 16.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 42 sq cm (b) 84 sq cm (c) 18 sq cm (d) 21 sq cm
17. 17.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
18. 18.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
19. 19.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
20. 20.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
21. 21.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
22. 22.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 217 sq cm (c) 36 sq cm (d) 144 sq cm
23. 23.A cuboid is 5 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 10 cu cm (b) 160 cu cm (c) 17 cu cm (d) 100 cu cm
24. 24.A cuboid is 9 cm long, 7 cm wide and 2 cm high. What is its total surface area? (a) 126 sq cm (b) 380 sq cm (c) 95 sq cm (d) 190 sq cm
25. 25.A cuboid is 8 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 360 sq cm (b) 144 sq cm (c) 90 sq cm (d) 180 sq cm
26. 26.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
27. 27.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
28. 28.A cuboid is 6 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 120 sq cm (b) 60 sq cm (c) 240 sq cm (d) 72 sq cm
29. 29.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 220 cm (d) 440 cm
30. 30.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
31. 31.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
32. 32.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) 3 times (c) 27 times (d) 6 times
33. 33.A cuboid is 12 cm long, 5 cm wide and 6 cm high. What is its volume? (a) 324 cu cm (b) 23 cu cm (c) 60 cu cm (d) 360 cu cm
34. 34.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 343 cu cm (c) 21 cu cm (d) 294 cu cm
35. 35.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 6 times (c) 3 times (d) 27 times
36. 36.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 24 cu cm (c) 8 cu cm (d) 16 cu cm
37. 37.A cuboid is 5 cm long, 3 cm wide and 10 cm high. What is its volume? (a) 150 cu cm (b) 18 cu cm (c) 190 cu cm (d) 15 cu cm
38. 38.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 176 cm (d) 88 cm
39. 39.A cube has edges of 9 cm. What is its volume? (a) 486 cu cm (b) 324 cu cm (c) 27 cu cm (d) 729 cu cm
40. 40.A cuboid is 8 cm long, 6 cm wide and 3 cm high. What is its total surface area? (a) 144 sq cm (b) 360 sq cm (c) 180 sq cm (d) 90 sq cm

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