Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 522 · 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 the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 3 times (c) 6 times (d) 27 times
2. 2.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
3. 3.A cuboid is 9 cm long, 4 cm wide and 9 cm high. What is its volume? (a) 22 cu cm (b) 306 cu cm (c) 36 cu cm (d) 324 cu cm
4. 4.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
5. 5.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 26 sq cm (b) 104 sq cm (c) 24 sq cm (d) 52 sq cm
6. 6.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 25 times (c) 5 times (d) 125 times
7. 7.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 2464 cm (d) 352 cm
8. 8.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) 2 times (c) 5 times (d) 8 times
9. 9.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
10. 10.If the radius of a circle 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
11. 11.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
12. 12.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
13. 13.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 132 sq cm
14. 14.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 616 sq cm
15. 15.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 16 cu cm (c) 8 cu cm (d) 24 cu cm
16. 16.A cuboid is 7 cm long, 5 cm wide and 5 cm high. What is its total surface area? (a) 95 sq cm (b) 175 sq cm (c) 380 sq cm (d) 190 sq cm
17. 17.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
18. 18.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
19. 19.A cuboid is 12 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 312 cu cm (b) 36 cu cm (c) 288 cu cm (d) 23 cu cm
20. 20.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 24 sq cm (c) 4 sq cm (d) 16 sq cm
21. 21.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 24 cu cm (c) 384 cu cm (d) 256 cu cm
22. 22.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 693 sq cm
23. 23.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
24. 24.A cuboid is 7 cm long, 5 cm wide and 3 cm high. What is its total surface area? (a) 105 sq cm (b) 142 sq cm (c) 71 sq cm (d) 284 sq cm
25. 25.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 125 cu cm (c) 100 cu cm (d) 150 cu cm
26. 26.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 1331 cu cm (c) 726 cu cm (d) 33 cu cm
27. 27.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
28. 28.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
29. 29.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
30. 30.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) 27 times (c) 6 times (d) 9 times
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) 64 times (b) 8 times (c) 16 times (d) 4 times
32. 32.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) 4 times (c) 5 times (d) 2 times
33. 33.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 9 cu cm (c) 27 cu cm (d) 54 cu cm
34. 34.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) 16 times (c) 4 times (d) 64 times
35. 35.If the radius of a circle 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
36. 36.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 16 times (c) 64 times (d) 8 times
37. 37.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
38. 38.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) 125 times (c) 25 times (d) 10 times
39. 39.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) 25 times (c) 125 times (d) 10 times
40. 40.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 217 cu cm (c) 144 cu cm (d) 216 cu cm

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