Painting Bell TowersDate: 6/3/96 at 21:51:20 From: Robert Kellar Subject: Bell tower Problem Dear Dr. Math, I need the square footage needed to cover 3 bell towers. They will be gilded. The main dome is truncated with a radius of 20 feet (40 ft diameter) and is 14 feet high. The second is a 1/2 dome 13'4" high with a radius of 13' 4". The bell tower has an 8' radius (16" diameter) and is 5' 10" high. Please help me and hurry, I am in dire straits. Sincerely, Robert Kellar Date: 6/4/96 at 7:24:50 From: Doctor Anthony Subject: Re: Bell tower Problem A useful fact to remember is that the surface area of a spherical cap is equal to the curved surface area of an equal depth of a cylinder containing the sphere. So surface area of the first dome = 2*pi*20*14 = 560*pi. Surface area of the second dome = 2*pi*13.333*13.333 = 355.555*pi. Surface area of the third dome = 2*pi*8*5.833 = 93.333*pi. So the total surface area for all three = 1008.888*pi = 3169.552 square feet. -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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