From a solid cylinder of height $2.8 c m$ and diameter $4.2 c m$ , a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. (Take $π = 22 / 7$ )

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Solution

Total surface area = $C S A_{c o n e} + C S A_{c y l i n d e r} + A r e a_{c y l i n d e r t o p}$

= $π r l + 2 π r h + π r^{2}$

r= Radius of cone and cylinder $= 2.1 c m$ ; h = Height of cylinder and cone $= 2.8$ cm; l = Slant height of cone $= \sqrt{{2.1}^{2} + {2.8}^{2}} = 3.5 c m$

Hence TSA $= π r (l + 2 h + r) = 73.92 c m^{2}$

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From a solid cylinder of height 2.8cm and diameter 4.2cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. (Take π=22/7)

Total surface area = CSAcone+CSAcylinder+Areacylindertop=πrl+2πrh+πr2r= Radius of cone and cylinder=2.1cm; h = Height of cylinder and cone =2.8 cm; l = Slant height of cone =√2.12+2.82=3.5cmHence TSA =πr(l+2h+r)=73.92cm2

From a solid cylinder of height $2.8 c m$ and diameter $4.2 c m$ , a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. (Take $π = 22 / 7$ )