Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 811 · 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 11 cm. What is its volume? (a) 33 cu cm (b) 726 cu cm (c) 484 cu cm (d) 1331 cu cm
2. 2.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 343 cu cm (c) 294 cu cm (d) 196 cu cm
3. 3.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
4. 4.A cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 100 sq cm (c) 1000 sq cm (d) 400 sq cm
5. 5.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
6. 6.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 36 sq cm (c) 217 sq cm (d) 216 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 cuboid is 12 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 36 cu cm (b) 192 cu cm (c) 144 cu cm (d) 19 cu cm
9. 9.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) 8 times (c) 2 times (d) 4 times
10. 10.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 6 times (c) 3 times (d) 27 times
11. 11.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
12. 12.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 616 cm (d) 176 cm
13. 13.A cuboid is 9 cm long, 6 cm wide and 8 cm high. What is its total surface area? (a) 432 sq cm (b) 696 sq cm (c) 174 sq cm (d) 348 sq cm
14. 14.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 729 cu cm (c) 324 cu cm (d) 486 cu cm
15. 15.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
16. 16.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 176 sq cm
17. 17.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 176 sq cm
18. 18.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) 25 times (c) 125 times (d) 5 times
19. 19.A cuboid is 9 cm long, 8 cm wide and 4 cm high. What is its volume? (a) 288 cu cm (b) 280 cu cm (c) 21 cu cm (d) 72 cu cm
20. 20.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) 27 times (c) 3 times (d) 6 times
21. 21.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
22. 22.A cube has edges of 8 cm. What is its total surface area? (a) 256 sq cm (b) 512 sq cm (c) 64 sq cm (d) 384 sq cm
23. 23.A cuboid is 11 cm long, 4 cm wide and 10 cm high. What is its total surface area? (a) 194 sq cm (b) 440 sq cm (c) 388 sq cm (d) 776 sq cm
24. 24.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 44 cm (d) 616 cm
25. 25.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
26. 26.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
27. 27.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
28. 28.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
29. 29.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
30. 30.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 104 sq cm (b) 24 sq cm (c) 52 sq cm (d) 26 sq cm
31. 31.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 6 times (c) 2 times (d) 4 times
32. 32.A cuboid is 11 cm long, 6 cm wide and 4 cm high. What is its total surface area? (a) 268 sq cm (b) 134 sq cm (c) 264 sq cm (d) 536 sq cm
33. 33.A cuboid is 8 cm long, 6 cm wide and 9 cm high. What is its total surface area? (a) 432 sq cm (b) 174 sq cm (c) 696 sq cm (d) 348 sq cm
34. 34.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
35. 35.A cube has edges of 8 cm. What is its volume? (a) 256 cu cm (b) 512 cu cm (c) 24 cu cm (d) 384 cu cm
36. 36.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
37. 37.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
38. 38.A cuboid is 10 cm long, 4 cm wide and 4 cm high. What is its total surface area? (a) 384 sq cm (b) 160 sq cm (c) 192 sq cm (d) 96 sq cm
39. 39.A cube has edges of 4 cm. What is its volume? (a) 64 cu cm (b) 65 cu cm (c) 96 cu cm (d) 12 cu cm
40. 40.A cuboid is 7 cm long, 5 cm wide and 2 cm high. What is its volume? (a) 35 cu cm (b) 14 cu cm (c) 70 cu cm (d) 118 cu cm

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