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A grain silo consists of a cylindrical main section and a hemispherical roof. if the total volume of the silo (including the part inside the roof section) is 17,000 ft3 and the cylindrical part is 30 ft tall, what is the radius of the silo, correct to the nearest tenth of a foot? r = ft

Respuesta :

calculista
we know that
volume of a grain silo=volume of a cylinder+volume of a hemisphere
volume of a grain silo=17000 ft³

volume of a cylinder=pi*r²*h
h=30 ft
volume of a cylinder=pi*r²*30----> 30*pi*r² ft³

volume of a hemisphere=(2/3)*pi*r³
so
17000=30*pi*r²+(2/3)*pi*r³-----> multiply by 3---> 51000=282.60*r²+6.28*r³
6.28*r³+282.60*r²-51000=0

using a graph tool
see the attached figure

the solution is 
r=11.942 ft-------> r=11.9 ft

the answer is
The radius of the silo is 11.9 ft
Ver imagen calculista

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