A culvert is constructed out of large cylindrical shells cast in concrete, as shown in the figure. Using the formula for the volume of a cylinder given on the inside back cover of this book, explain why the volume of the cylindrical shell is V = πR2h − πr2h. Factor to show that V = 2π · average radius · height · thickness Since average radius = Incorrect: Your answer is incorrect. , height = h, and thickness = Incorrect: Your answer is incorrect. , we see the following. V = πR2h − πr2h = 2πh 2 = 2πh(R − r) 2 = 2π · 2 · h · R − r = 2π · average radius · height

Question

A culvert is constructed out of large cylindrical shells cast in concrete, as shown in the figure.  Using the formula for the volume of a cylinder given on the inside back cover of this book, explain why the volume of the cylindrical shell is V = πR2h − πr2h.  Factor to show that V = 2π · average radius · height · thickness   Since average radius =	  Incorrect: Your answer is incorrect. ,	height = h,	and thickness =	  Incorrect: Your answer is incorrect. ,	we see the following.	 V	 = 	πR2h − πr2h  = 	2πh    2   = 	2πh(R − r)    2   = 	2π	·	   2 ·	h ·	  R − r	   = 	2π · average radius · height