A-solid-cone-of-height-56cm-and-a-basem-diaeter-of-56cm-is-formed-from-al-cylindrica-drum-equal-in-height-andt-diameer-with-the-cone-Find-the-surfacee-ara-of-the-remaining-part-of-the-drum-if-the

Question Number 180191 by cherokeesay last updated on 08/Nov/22

$$ \\ $$$$\mathrm{A}\:\mathrm{solid}\:\mathrm{cone}\:\mathrm{of}\:\mathrm{height}\:\mathrm{56cm}\:\mathrm{and}\:\mathrm{a}\:\mathrm{basem} \\ $$$$\mathrm{diaeter}\:\mathrm{of}\:\mathrm{56cm}\:\mathrm{is}\:\mathrm{formed}\:\mathrm{from}\:\mathrm{al} \\ $$$$\mathrm{cylindrica}\:\mathrm{drum}\:\mathrm{equal}\:\mathrm{in}\:\mathrm{height}\:\mathrm{andt} \\ $$$$\mathrm{diameer}\:\mathrm{with}\:\mathrm{the}\:\mathrm{cone}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{surfacee} \\ $$$$\mathrm{ara}\:\mathrm{of}\:\mathrm{the}\:\mathrm{remaining}\:\mathrm{part}\:\mathrm{of}\:\mathrm{the}\:\mathrm{drum}. \\ $$$$ \\ $$$$\left(\mathrm{if}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{is}\:\mathrm{accompanied}\:\mathrm{by}\:\mathrm{a}\:\right. \\ $$$$\mathrm{diagramit}\:\mathrm{will}\:\mathrm{be}\:\mathrm{perfect}\:\mathrm{and}\:\mathrm{I}\:\mathrm{thank}\:\mathrm{youo} \\ $$$$\left.\mathrm{fr}\:\mathrm{it}\right). \\ $$

Answered by Acem last updated on 09/Nov/22

$${As}\:{i}\:{got}\:{that}\:{we}\:{formed}\:{a}\:{cone}\:{from} \\ $$$${a}\:{cylindric}\:{drum}…\:{right}?\:{at}\:{this}\:{case}\:{the}\:{surface} \\ $$$$\:{consists}\:{of}\:{three}\:{surfaces}: \\ $$$$\:{upper}\:{base},\:{external}\:{side}\:{and}\:{internal}\:{one} \\ $$$$\:{S}=\:\mathrm{0}.\mathrm{25}\pi{D}^{\mathrm{2}} \:+\:\pi{Dh}\:+\:\mathrm{0}.\mathrm{5}\pi{D}\:\sqrt{\mathrm{0}.\mathrm{25}{D}^{\mathrm{2}} +{h}^{\mathrm{2}} } \\ $$$$\:{S}=\:\pi{D}\:\left(\mathrm{0}.\mathrm{25}{D}+\:{h}+\:\mathrm{0}.\mathrm{25}\:\sqrt{{D}^{\mathrm{2}} +\:\mathrm{4}\:{h}^{\mathrm{2}} }\right) \\ $$$$\:{S}\approx\:\mathrm{1}.\mathrm{782}\:{m}^{\mathrm{2}} \\ $$$$\: \\ $$

Commented by Acem last updated on 08/Nov/22