Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 16 · 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.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) 25 times (c) 5 times (d) 10 times
2. 2.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 264 cm (d) 1386 cm
3. 3.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
4. 4.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
5. 5.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 24 cu cm (c) 6 cu cm (d) 8 cu cm
6. 6.A cube has edges of 7 cm. What is its total surface area? (a) 343 sq cm (b) 49 sq cm (c) 196 sq cm (d) 294 sq cm
7. 7.A cuboid is 4 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 124 sq cm (b) 62 sq cm (c) 72 sq cm (d) 248 sq cm
8. 8.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) 2 times (c) 8 times (d) 4 times
9. 9.If the radius of a circle 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
10. 10.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 616 sq cm (d) 44 sq cm
11. 11.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) 4 times (c) 64 times (d) 8 times
12. 12.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
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) 5 times (b) 8 times (c) 2 times (d) 4 times
14. 14.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
15. 15.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 440 cm (d) 220 cm
16. 16.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
17. 17.A cuboid is 10 cm long, 4 cm wide and 4 cm high. What is its volume? (a) 18 cu cm (b) 192 cu cm (c) 160 cu cm (d) 40 cu cm
18. 18.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 44 sq cm (d) 77 sq cm
19. 19.A cuboid is 6 cm long, 5 cm wide and 8 cm high. What is its volume? (a) 19 cu cm (b) 240 cu cm (c) 30 cu cm (d) 236 cu cm
20. 20.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 5544 sq cm
21. 21.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 33 cu cm (c) 726 cu cm (d) 1331 cu cm
22. 22.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
23. 23.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) 8 times (c) 16 times (d) 64 times
24. 24.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 616 sq cm (d) 88 sq cm
25. 25.A cuboid is 9 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 246 sq cm (b) 216 sq cm (c) 123 sq cm (d) 492 sq cm
26. 26.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 324 sq cm (c) 729 sq cm (d) 486 sq cm
27. 27.A cuboid is 6 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 12 cu cm (b) 90 cu cm (c) 54 cu cm (d) 18 cu cm
28. 28.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 512 cu cm (c) 256 cu cm (d) 24 cu cm
29. 29.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
30. 30.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 88 cm (d) 44 cm
31. 31.A cuboid is 11 cm long, 5 cm wide and 4 cm high. What is its volume? (a) 20 cu cm (b) 220 cu cm (c) 55 cu cm (d) 238 cu cm
32. 32.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 6 cu cm (b) 14 cu cm (c) 54 cu cm (d) 102 cu cm
33. 33.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 9 cu cm (c) 36 cu cm (d) 54 cu cm
34. 34.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 88 cm (d) 2464 cm
35. 35.A cuboid is 11 cm long, 4 cm wide and 4 cm high. What is its total surface area? (a) 416 sq cm (b) 104 sq cm (c) 176 sq cm (d) 208 sq cm
36. 36.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 8 times (c) 4 times (d) 64 times
37. 37.A cuboid is 9 cm long, 7 cm wide and 9 cm high. What is its total surface area? (a) 828 sq cm (b) 414 sq cm (c) 207 sq cm (d) 567 sq cm
38. 38.A cuboid is 5 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 73 sq cm (b) 90 sq cm (c) 292 sq cm (d) 146 sq cm
39. 39.A cuboid is 9 cm long, 4 cm wide and 8 cm high. What is its volume? (a) 36 cu cm (b) 288 cu cm (c) 280 cu cm (d) 21 cu cm
40. 40.A cuboid is 9 cm long, 5 cm wide and 8 cm high. What is its total surface area? (a) 157 sq cm (b) 314 sq cm (c) 360 sq cm (d) 628 sq cm

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