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A woodern article was made by scooping out a hemisphere from each end of a soid cylinder is 12 cm and its base is of radius 4.2 cm find the total suface area of the article. Also find the volume of the wood left in the article. |
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Answer» Solution :RADIUS of the hemisphere r= 4.2 CM Radius of the cylinder r= 4.2 cm Height of the cylinder , h= 12 cm Total surface area of the article = curved surface area of cylinder + curved surface area of 2 hemispheres `= 2pi r h + 2 xx 2pi r^2 = 2pi RH + 4 pi r^2 ` `=2pir(h+2r)=[2xx22/7xx4.2 xx(12-4/3xx4.2)]cm^2` `= (26.4 xx 20.4)cm^3= 354.816 cm^3` Total volume of the wood left in the article = volume of the cylinder - volume of 2 hemispheres `pi r^2h -2 xx 2/3pi r^3= pi r^2(h-4/3r)` `[ 22/7xx 4.2 xx 4.2 xx(12 - 4/3xx 4.2)]cm^3 ` `=(55.44 xx 6.4 )cm^2= 354.816 cm^3` (`##RSA_MATH_X_C17_S01_020_S01.png" width="80%"> |
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