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

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