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November 15th, 2011, 01:35 PM  #1 
Newbie Joined: Aug 2011 Posts: 24 Thanks: 0  Find the Surface Area of an Opentopped Lid
Find the surface area of this opentopped lid. I know the formula for the surface area of a cylinder is 2pi(r^2)+2pi(rh), but I don't know how to calculate the inside of the lid. 
November 15th, 2011, 02:10 PM  #2 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: Find the Surface Area of an Opentopped Lid [color=#000000]The total area is .[/color] 
November 15th, 2011, 03:15 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 18,704 Thanks: 1528 
That can't be right.

November 15th, 2011, 05:43 PM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,847 Thanks: 766  Re: Find the Surface Area of an Opentopped Lid
Hard to tell...if you mean the outside plus the inside: bottom: 2(50^2)pi = 5000pi : (outside bottom) + (inside bottom + 1cm ring) outside wall: 2(50)(500)pi = 50000pi inside wall: 2(49)(500)pi = 49000pi Add 'em up: 104000pi ZardoZ used 99 as inside diameter: should be 98 
November 15th, 2011, 07:23 PM  #5  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407  Re: Find the Surface Area of an Opentopped Lid Hello, Pumpkin99 I wish you would explain this "opentopped lid" more clearly. Quote:
I would expect a "lid" to be like a pizza pan . . . flat bottom (or top), round, with short vertical sides. You've given us a cylinder: 100 cm wide and 500 cm high, with a "wall" that is 1 cm thick. You say "opentopped", so I assume it has a "floor" (with thickness 1 cm). I assume that we want to paint this thing, so we want to know [color=beige]. . [/color] the number of square centimeters of paint we will need. The side view of this "lid" looks like this: Code: 1 1 ** : **   :     :     :    499 :   500  :     : 49    *+*   : 50  ** Outside area On the top we have a "ring" with area:[color=beige] .[/color] On the "side", we have the curved area:[color=beige] .[/color] On the bottom, we have a circle of radius 50:[color=beige] .[/color] Inside area On the "side" we have the curved area:[color=beige] .[/color] On the bottom, we have a circle of radius 49:[color=beige] .[/color] The total surface area is:[color=beige] .[/color]  
November 15th, 2011, 11:37 PM  #6 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: Find the Surface Area of an Opentopped Lid [color=#000000]Seems I had a different shape in mind! When you don't use pencil and paper and use only the mind this happens, seems I am not clever enough! [/color] 
November 16th, 2011, 03:28 AM  #7  
Global Moderator Joined: Dec 2006 Posts: 18,704 Thanks: 1528  Quote:
 
November 16th, 2011, 08:02 AM  #8 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,847 Thanks: 766  Re: Find the Surface Area of an Opentopped Lid
Plus a "lid" is a "cover": "a removable or hinged cover for closing the opening, usually at the top, of a pot, jar, trunk, etc" So a lid with "walls" of length 500 cm sure seems strange; wonder if he means .5 cm 

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area, find, lid, opentopped, surface 
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