Plane and solid geometry . 554. Def. This constant ratio of the circumference ot acircle to its diameter is usually represented by the Greek let-ter TT. It will be shown (§ 568) that its value is approxi-mately 34; or, more accurately, 555. Cor. I. TlxecirczunferenceofacircleiseqiialtoSirR. 556. Cor. n. Any two circumferences are to eachother as their radii, Ex. 1002. If the radius of a wheel is 4 feet, how far does it roll intwo revolutions ? Ex. 1003. How many revolutions are made by a wheel whose radiusis 3 feet in rolling 44 yards ? Ex. 1004. (a) Find the width of the ring between
Plane and solid geometry . 554. Def. This constant ratio of the circumference ot acircle to its diameter is usually represented by the Greek let-ter TT. It will be shown (§ 568) that its value is approxi-mately 34; or, more accurately, 555. Cor. I. TlxecirczunferenceofacircleiseqiialtoSirR. 556. Cor. n. Any two circumferences are to eachother as their radii, Ex. 1002. If the radius of a wheel is 4 feet, how far does it roll intwo revolutions ? Ex. 1003. How many revolutions are made by a wheel whose radiusis 3 feet in rolling 44 yards ? Ex. 1004. (a) Find the width of the ring between two concentriccircumferences whose lengths are 2 feet and 8 feet, respectively. (&) Assuming the earths equator to be 25,000 miles, find the widthof the ring between it and a concentric circumference 1 foot longer. (c) Write your inference in the form of a general statement. 266 PLANE GEOMETRY Proposition XIII. Theorem 557. Tlw area of a regular polygon is equal to onehalf the product of its perimeter and its Given regular polygon ABCD • •apothem. To prove area of ABCD . • = ^ P r. Argument 1. In polygon ABCD • •«, inscribe a circle. 2. Then r, the apothem of regular polygon ABCD. • •, is the radius of circle 0. 3. .-. area of ABCD -- - = ^ P r. P its perimeter, and r its Reasons 1. § 530. 2. § 533. 3. § 492. Ex. 1005. Find the area of a regular hexagon whose side is 6 inches. Ex. 1006. The area of an inscribed regular hex-agon is a mean proportional between the areas of theinscribed and circumscribed equilateral triangles. Ex. 1007. The figure represents a flower beddrawn to the scale of 1 inch to 20 feet. Find thenumber of square feet in the flower bed.
Size: 1609px × 1552px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
