9. The diameter of the sun is 883,320 miles: what is its circumference? = 883320 X 3.14159 2775'029; or 883320 X 227 2776.148. 10. If the equatorial diameter be 79249 miles, chat is the length of a degree at the equator? Circumference at equator = 79249 X 22 ÷ 7 =24906.8. A degree 2.4,906·8÷360 = = or 79249 X 3'14159 24896.78, and a degree 24896.78 360 = 69.15. 11. Find the radii of the inscribed and circumscribed circles and the areas of the following regular polygons : = (1). Triangle; side = 10. Inscribed rad. = 7. Circumscribed rad. 5'77350 Ans. Area. 85065 43.30127 I'72048 64'9519 43'455843 377'01623 (6). 18.66025 19.31852 1119.61524 12. What is the diameter of a stone column whose circumference measures 16 ft. 6 in. ? Hence area of the segment of each circle cut off by their common chord 104.76 · 43°3 61.46. Therefore the area of the part common to both circles 122'92. Each of the other parts 5. The radius of a circle circumscribing a hexagon is 14 in.: find the radius of the inscribed circle and the area of the hexagon. The radius of the inscribed circle is the height of an equilateral triangle whose side is 14 in ; or r = 7√3 = Area 6 X 7 X 7 √ 3 12.1243556. = 509 222935. 6. The side of an octagon is 5 ft.: find the radius of the inscribed circle and the area. The side of the square formed by producing alternate sides of the octagon is 5 + 2 x, where a2 + x2 = 25 or x = 3.535. Hence the radius of the inscribed circle, which is half the side, = 6·035. The × 8 × 5 × 6·035 = 120.7106. 124 area = == 7. If the diameter of a circle be 10, find the side of a square having the same area. 8. Find the length of a side of a square equal in area to a circle whose circumference is 20 ft. MAXIMA AND MINIMA. (CHAP. XV. Page 229.) 1. If the diameter of a well be 3 ft. 9 in., what is its circumference? 22 Circum. = of 45 in. 11 ft. 9 in. 7 2. The diameter of a circular plantation is 100 yards: how many yards of fencing would be required to enclose it? 22 Circum. = of 100 = 314 yds. 7 3. If the radius of a circle be 10, what are the sides of a regular inscribed pentagon, hexagon, octagon, and decagon? Apply Solution of Ex. 1, page 222. Answer. Decagon 6.18034. Octagon 7.6536. Hexagon 10. Pentagon 117557. 4. If the centre of a circle whose diameter is 20 be in the circumference of another circle whose diameter is also 20, what will be the areas of the three included spaces. Area of a third of each circle 7 Diameter = of 161 ft. = 22 5 ft. 3 in. 13. If the circumference of the earth be 25,000 miles, what is its diameter, supposing it to be a sphere? 7 Diameter = of 22 25,000 7954 miles. 14. The diameters of two concentric circles being 15 and 9, required the area of the ring contained between their circumferences. 15. What is the area of the ring, the two diameters being 10 and 20? 16. A mason is to put a stone curb to a round well at 8d. per square foot; the breadth of the curb is to be 10 in. and the diameter of the well 3ft: what will be the expense? 17. Four men bought a grindstone of 60 in. diameter, each paying a quarter of the expense: supposing they use the stone in succession, what part of the diameter ought the first and the last to grind down? Let 2. be the diameter of the last portion; Let 2 y be the portion of the diameter used by 4 019238 inches. Therefore 2 y = 8.038476 and 2 x = 30. 18. Find the area of a circle whose diameter is 7. 19. How many square yards are in a circle whose diameter is 3 ft.? 22 Area = X sqr. ft. 9.625 sqr. ft. 7 49 = 1069 sqr. yds. 20. Find the area of a circle whose circumference is 12 ft. |