AMSCO'S Geometry. New York - Rye High School

454 The Geometry of Three DimensionsEXAMPLE 1Solution a.Surface Area and Volume of a Circular CylinderThe label on a cylindrical can of soupis a rectangle whose length is the circumferenceof the base of the canrand whose width is the height of the hcan. This label is equal in area to the SOUPSOUPlateral surface of the cylindrical can. In2rExercise 12 of Section 11-5, you provedthat the lateral area, A, of a right prism is the product of the perimeter, p, of theprism and the height, h p, of the prism (A ph p). The circumference of the baseof a cylinder corresponds to the perimeter of the base of a prism. Therefore, wecan say that the area of the lateral surface of a right circular cylinder is equal tothe circumference of the circular base times the height of the cylinder.If a right circular cylinder has bases that are circles of radius r and height h,then:The lateral area of the cylinder 2prhThe total surface area of the cylinder 2prh 2pr 2The volume of the cylinder Bh pr 2 hNote: The volume of any circular cylindar is pr 2 h.Jenny wants to build a right circular cylinder out of cardboard with bases thathave a radius of 6.0 centimeters and a height of 14 centimeters.a. How many square centimeters of cardboard are needed for the cylinder tothe nearest square centimeter?b. What will be the volume of the cylinder to the nearest cubic centimeter?A 5 2prh 1 2pr 25 2p(6.0)(14) 1 2p(6.0) 25 168p 172p5 240p cm 2Express this result as a rational approximation rounded to the nearestsquare centimeter.240p 753.9822369 754 cm 2b. V 5pr 2 h5p(6.0) 2 (14)5 504p cm 3