Question Number 3950 by Rasheed Soomro last updated on 25/Dec/15
$$\mathcal{W}{e}\:{can}\:{make}\:{a}\:\boldsymbol{{cyllinder}}\:{from}\:{a} \\ $$$$\boldsymbol{{rectangle}}\:{by}\:{connecting}\:{its}\:{opposite} \\ $$$$\boldsymbol{{edges}}. \\ $$$${Suppose}\:{we}\:{have}\:{two}\:{copies}\:{of}\:{a} \\ $$$$\boldsymbol{{non}}−\boldsymbol{{square}}\:\boldsymbol{{rectangle}}.{From} \\ $$$${one}\:{copy}\:{we}\:{make}\:{a}\:{long}\:{cyllinder} \\ $$$${by}\:{connecting}\:{long}\:{edges}\:{of}\:{it}\: \\ $$$${whereas}\:{from}\:{other}\:{copy}\:{by}\:{connecting} \\ $$$${short}\:{edges}\:{a}\:{short}\:{cyllinder}\:{is}\:{made}. \\ $$$${Compare}\:{the}\:\boldsymbol{{volumes}}\:{of}\:{these}\:{two} \\ $$$${cyllinders}. \\ $$
Answered by prakash jain last updated on 25/Dec/15
$${a}={length},\:{b}\:{width} \\ $$$${case}\:{i}:\:{radius}=\frac{{a}}{\mathrm{2}\pi},\:\mathrm{volume}=\pi\frac{{a}^{\mathrm{2}} }{\mathrm{4}\pi^{\mathrm{2}} }{b}=\frac{{a}^{\mathrm{2}} {b}}{\mathrm{4}\pi} \\ $$$${case}\:{ii}:\:{radius}=\frac{{b}}{\mathrm{2}\pi},\:\mathrm{volume}=\pi\frac{{b}^{\mathrm{2}} }{\mathrm{4}\pi^{\mathrm{2}} }{a}=\frac{{b}^{\mathrm{2}} {a}}{\mathrm{4}\pi} \\ $$$${ratio}=\frac{{a}}{{b}} \\ $$
Commented by Rasheed Soomro last updated on 25/Dec/15
$$\boldsymbol{{T}}\:{h}\:\alpha\:{n}\:\boldsymbol{{k}\mathcal{S}}! \\ $$$${It}\:{means}\:{cyllinder}\:{of}\:{greater}\:{height}\:{has}\: \\ $$$${small}\:{volume}. \\ $$$$\frac{{Cyllinder}\:{of}\:{height}\:{b}}{{Cyllinder}\:{of}\:{height}\:{a}}=\frac{{a}}{{b}} \\ $$