The right circular cone is enveloping …
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The right circular cone is enveloping a right circular cylindersuch that the radius of the base of cylinder rests on the base of cone If the radius and height of cone is 4cm and 10cm.Find CSA of the largest cylinder that can be enveloped by the cone.
Posted by Jd Shukla 8 years, 9 months ago
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Neeraj Sharma 8 years, 9 months ago
{tex}let\,radius\,of\,cylinder\,is\,r{/tex}
{tex}so\,PE = r\,cm{/tex}
{tex}let\,AP = h\,cm{/tex}
{tex}then\,PQ = \left( {10 - h} \right)cm{/tex}
{tex}\sin ce\,\Delta APE \sim \Delta AQC{/tex}
{tex}So,{/tex}
{tex}{{AP} \over {AQ}} = {{PE} \over {QC}}{/tex}
{tex}{h \over {10}} = {r \over 4}{/tex}
{tex}h = {{10r} \over 4}{/tex}
{tex}so,\,PQ = 10 - {{10r} \over 4} = \left( {10 - {{5r} \over 2}} \right)cm{/tex}
{tex}CSA\,of\,cylinder = 2\pi r\left( {10 - {{5r} \over 2}} \right){/tex}
{tex} = \pi r\left( {20 - 5r} \right){/tex}
{tex} = 5\pi r\left( {4 - r} \right)c{m^2}{/tex}
Largest possible curved surface area of cylinder={tex}5\pi r\left( {4 - r} \right)c{m^2}{/tex}
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