Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 606 · 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.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
2. 2.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 9856 sq cm
3. 3.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 1386 cm (d) 264 cm
4. 4.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) 125 times (c) 10 times (d) 5 times
5. 5.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 176 cm (d) 88 cm
6. 6.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
7. 7.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
8. 8.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 693 sq cm (d) 5544 sq cm
9. 9.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 22 cm (d) 154 cm
10. 10.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
11. 11.A cuboid is 12 cm long, 11 cm wide and 4 cm high. What is its total surface area? (a) 448 sq cm (b) 896 sq cm (c) 528 sq cm (d) 224 sq cm
12. 12.A cuboid is 9 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 80 cu cm (b) 13 cu cm (c) 36 cu cm (d) 18 cu cm
13. 13.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
14. 14.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 8 times (c) 4 times (d) 5 times
15. 15.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 308 sq cm (d) 2464 sq cm
16. 16.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 486 cu cm (c) 324 cu cm (d) 729 cu cm
17. 17.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
18. 18.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) 9 times (d) 3 times
19. 19.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
20. 20.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
21. 21.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
22. 22.A cuboid is 7 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 28 cu cm (b) 14 cu cm (c) 122 cu cm (d) 84 cu cm
23. 23.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
24. 24.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 343 cu cm (c) 196 cu cm (d) 294 cu cm
25. 25.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
26. 26.If the side of a square 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
27. 27.If the radius of a circle 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
28. 28.A cuboid is 8 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 14 cu cm (b) 32 cu cm (c) 64 cu cm (d) 112 cu cm
29. 29.If the side of a square 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
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) 6 times (b) 27 times (c) 9 times (d) 3 times
31. 31.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) 8 times (c) 16 times (d) 64 times
32. 32.A cuboid is 10 cm long, 8 cm wide and 4 cm high. What is its volume? (a) 80 cu cm (b) 304 cu cm (c) 320 cu cm (d) 22 cu cm
33. 33.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 6 cu cm (c) 16 cu cm (d) 24 cu cm
34. 34.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 9 times (d) 6 times
35. 35.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 4 times (c) 16 times (d) 8 times
36. 36.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) 5 times (c) 25 times (d) 125 times
37. 37.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 1386 sq cm
38. 38.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) 4 times (c) 8 times (d) 16 times
39. 39.A cube has edges of 5 cm. What is its volume? (a) 100 cu cm (b) 150 cu cm (c) 125 cu cm (d) 15 cu cm
40. 40.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

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