EL L. Yad the wa of a drie whose fameter is 256. To find the diameter of a circle when the area is given. Multiply the area by 14 and divide by 11, and extract the square root. Ex. The area of a circle is 240.7.6 square feet; find To find the area of a circular ring. Multiply the sum of the inner and outer diameters by their difference; then multiply by 11 and divide by 14. Ex. Find the area of a circular ring, whose inner and outer diameters are 12 and 20. To find the area of a circular sector. Multiply the circular measure of the angle subtended by the arc by the square of the radius, and divide by 2. Ex. Find the area of a circular sector whose radius is 28, and which contains an angle of 50° 36′. Circular Measure = '883 282=784 3532 7064 6181 2 692.272 346 136 Ans. I. 2. EXAMPLES. Find the area of a circle whose diameter is 56. Ans. 2464. Find the area of a circle whose diameter is 13 ft. 4 in. 3. Find the area of a circle whose diameter is 24 poles. 4. 5. is 47. Find the area of a circle whose diameter is 34 ft. 10 in. Find the circumference of a circle whose diameter Ans. 1475 Ans. 78 ft. 10 in. 6. Find the circumference of a circle whose diameter is 25 ft. 1 in. 7. Find the diameter of a circle whose circumference is 20 ft. 2 in. 8. The radius of a circle is 9 feet; find the length of an arc which contains 24°. Ans. 333 ft. 9. The radius of a circle is 3 feet; find the length of an arc which contains 36° 17'. Ans. 19 ft. IO. links. Find the area of a circle whose diameter is 476 II. Find the diameter of a circle whose area is 386. o. 10 square feet. Ans. 22 ft. 2 in. 12. Find the diameter of a circle whose area is 76 11 a. 3 r. 28725 P. Find the circumference of a circle whose diameter 13. is 12 ft. 6 in. 14. Find the area of a circular ring whose inner and outer diameters are 13 ft. 8 in. and 7 ft. 6 in. Ans. 102. 6.8 feet. 15. The radius of a circle is 12; find the area of a sector which contains 15° 20′. Ans. 19.274. 16. The radius of a circle is 9 feet; find the area of Ans. 243 feet. a sector which contains 35°. 17. The radius of a circle is 37 ft. 4 in.; find the area of a sector which is of a quadrant. Ans. 1368 feet. 18. Find the area of a circular ring whose inner diameter is 6 chains 25 links, and outer diameter 10 chains 35 links. Ans. 5 a. Ir. 15 P. 19. The radius of a circle is 17 ft. 3 in.; find the area of a sector which contains 24° 25'. Ans. 63 425 feet. 20. The area of a circular sector is 34%, and it contains an angle of 11° 15'; find the radius. Ans. 183. Let ACB be a semicircle, of which AB is the diameter, and let CD be perpendicular to AB. Then AD is called the abscissa, and CD the ordinate of the point C; and by a property of the circle, AD× DB = CD2, or CD = √ (AD × DB). |