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Painting Bell Towers

Date: 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.

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
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Associated Topics:
High School Geometry
High School Higher-Dimensional Geometry

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