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?
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
