. Complete arithmetic . , or ft. EXERCISE 119 Using 31^ find the circumferencey given the diameter: 1. 105 ft. 3. ft. 5. in. 7. 4970 in. 2. ft. 4. ft. 6. 4270 in. 8. in. Using 3~, find the circumference, given the radius: 9. 63 in. 11. 98 in. 13. in. 15. ft. 10. 77 in. 12. 210 in. 14. in. 16. ft. Using , find the circumference, given the diameter: 17. 27 ft. 19. 32 yd. 21. ft. 23. ft. 18. 43 ft. 20. yd. 22. ft. 24. in. Using , find the circumference, given the radius: 25. 27 in. 27. 61 in. 29. yd.
. Complete arithmetic . , or ft. EXERCISE 119 Using 31^ find the circumferencey given the diameter: 1. 105 ft. 3. ft. 5. in. 7. 4970 in. 2. ft. 4. ft. 6. 4270 in. 8. in. Using 3~, find the circumference, given the radius: 9. 63 in. 11. 98 in. 13. in. 15. ft. 10. 77 in. 12. 210 in. 14. in. 16. ft. Using , find the circumference, given the diameter: 17. 27 ft. 19. 32 yd. 21. ft. 23. ft. 18. 43 ft. 20. yd. 22. ft. 24. in. Using , find the circumference, given the radius: 25. 27 in. 27. 61 in. 29. yd. 31. ft. 26. 38 in. 28. ft. 30. yd. 32. ft. Using ^6, find the diameter, given the circumference:33. ft. 34. in. 35. in. 224 PRACTICAL MEASUREMENTS 230. Area of a Circle. We may cut a circle as here shownand separate it into a series of figures that are trianglesexcept for their curved bases. If we should call these fig-ures triangles their altitudes would be the radius of the. circle, and the sum of their bases would be the circumfer-ence. The area of each triangle (§ 225) equals half theproduct of the numbers representing the base and their total area equals half the product of thenumbers representing the circumference and radius. In geometry this is proved exactly, but this explanation is enoughfor our purpose. Thus, if the radius is 2 in. and the circumference (§229) is in.,the area is i of 2 x sq. in., or in. The area of a circle equals half the product of the numbersrepresenting the circumference and radius. 231. Area in Terms of Radius. We have found that area = | X radius x circumference (§ 230)and circumference = x 2 x radius (§ 229) ; therefore area = \X radius x x 2 x radius, or, canceling, area = x square of radius. Therefore, the area of a circle equals times thesquare of the radius. For example, if the radius is 2 in., the area is x 4
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