Shanta runs an industry in a shed which is in the shape of a cuboid surmounted by a half cylinder. If the base of the shed is of dimension `7m"\ "xx"\ "15 m` , and the height of the cuboidal portion is 8 m, find the volume of air that the shed

Explanation

The shed consits of a cuboid with dimensions l= 15 m, b= 7 m , h= 8 cm and a half -cylinder of radius, r = 7/2 m and height , H = 15 m
(i) Volume of air that the shed can hold
= volume of the cuboid `+ 1/2 xx` volume of the cylinder
`=lbh + 1/2 pi r^2 H =(15 xx 7 xx 8 + 1/2xx 22/7 xx 7/2 xx 7/2 xx 15 )m^3`
`= (840 + 1155/4)m^2 = ((4515)/(4)) m^3`
`=1128.75 m^3`
(ii) Total space occupied by machinery and 20 workers
`=(300 + 0.08 xx 20 )m^3= 301.6 m^3= 301. m^3`
Volume of air in the shed when there are machinery and workers inside it `= (1128. 75 - 301 .6 )cm^3 `
(iii) Total internal surface area of the shed (excluding floor)
= (surface area of walls )+ (surface area of ceiling )
= (area of two walls each measuring 15 m `xx` 8 m )+ (area of two walls each measuring 7 m `xx` 8 m )+ (area of two semicircles each of rasius 3.5 m) + (curved surface area`pirh` of half - cylinder)
`=[(2xx15 xx 8 )+(2xx7 xx8)+(2xx1/2xx22/7 xx7/2xx7/2)+(22/7xx7/2xx15 )]m^2`
`= (240 + 112 + 38.5 + 165 )m^2 = 555.5 m^2`
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