SOLUTION: What is the approximate surface area of the observatory if the radius is 10 ft and its altitude measures 24 ft

Algebra ->  Angles -> SOLUTION: What is the approximate surface area of the observatory if the radius is 10 ft and its altitude measures 24 ft       Log On


   

Question 157683: What is the approximate surface area of the observatory if the radius is 10 ft and its altitude measures 24 ft
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming the building is a cylinder with a hemisphere roof.
The cylinder surface are is the perimeter of the circle (hemisphere) multiplied by the height of the cylinder.
The height of the cylinder is the total height minus the hemisphere radius.
SA%5Bc%5D=2%2Api%2AR%2A%28H%5Bt%5D-R%29
SA%5Bc%5D=2%2Api%2A10%2A%2824-10%29
SA%5Bc%5D=2%2Api%2A10%2A%2814%29
SA%5Bc%5D=280%2Api
The surface area of the hemisphere is 1/2 the surface area of a sphere with radius 10 ft.
SA%5Bs%5D=%281%2F2%29%2A4%2Api%2AR%5E2
SA%5Bs%5D=2%2Api%2A10%5E2
SA%5Bs%5D=200%2Api
THe total surface is the sum of these two.
SA%5Bt%5D=SA%5Bc%5D%2BSA%5Bs%5D
SA%5Bt%5D=280%2Api%2B200%2Api
SA%5Bt%5D=480%2Api
or approximately
SA%5Bt%5D=1508
1508 sq. ft.