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A fabricator is hired to make a 27 foot long solid metal railing for the stairs at a local library. the railing is 2.5 inches high and 2.5 inches wide and is comprised of a rectangular prism and a half cylinder. how much metal, to the nearest cubic inch, will the railing contain?

Respuesta :

calculista
the complete question in the attached figure

we know that
volume of the railing=volume of a rectangular prism+volume a half cylinder

convert 27 ft to inches--------> 27*12-----> 324 in
step 1
find the volume of a rectangular prism
volume of a rectangular prism=L*W*H-----> 324*2.5*1.25-----> 1012.5 in³

step 2
find volume a half cylinder
volume a half cylinder=(1/2)*pi*r²*h
r=1.25 in
h= 324 in
volume a half cylinder=(1/2)*pi*1.25²*324---> 795.22 in³

step 3
volume of the railing=volume of a rectangular prism+volume a half cylinder
volume of the railing=1012.5+795.22------>1807.72  in³------> 1808 in³

the answer is
1808 in³

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