A pottery manufacturer has an order to manufacture 5,000 hanging vases each to hold 1/6 pt of water when full. The
vases are designed so as to fit int the corner of the room. The faces of each vase are triangular in shape and intersect to
form a pointed bottom. the area of polygon cut out of the plane of the base by lateral faces is 3 sq. in. The height of the
vase is 8 in. Compute the weight of pottery required if pottery weighs 130 lb. per cu.ft.
"V_ {out}= \\dfrac{1}{3}Sh=\\dfrac{1}{3}(3in^2)(8in)=8in^3V \nout\n\u200b\n = \n3\n1\n\u200b\n Sh= \n3\n1\n\u200b\n (3in ^\n2\n )(8in)=8in ^\n3"
Vase holds 1/4 pt. of water when full.
"3V \nin\n\u200b\n =\\frac{1}{4} pt=7.21875in ^\n3"
Then:
"V=V \nout\n\u200b\n \u2212V \nin\n\u200b\n \n=8in^3-7.21875in^3=0.78125in^3=8in ^\n3\n \u22127.21875in ^\n3\n =0.78125in \n3\n \n1 lbs\/ft ^3=\\frac{453.59237 g}{1728in^3}1lbs\/ft \n3\n =\\frac{453.59237g}{1728in ^\n3}\\\\Mvase\n =130( \\frac{\n1728in ^\n3}{\n \n453.59237g\n\u200b}\n )(0.78125in \n3\n )=26.6597g\nM=5000(26.6597g)=133298.540gM=5000(26.6597g)=133298.540g"
"M=5000(26.6597g)=133298.540g=133.299kg"
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