Question 1132645

<a href="http://tinypic.com?ref=8yvosl" target="_blank"><img src="http://i68.tinypic.com/8yvosl.gif" border="0" alt="Image and video hosting by TinyPic"></a>


given:

slant height {{{s=9r }}}

the height {{{h=12sqrt(5)}}}

{{{V=(pir^2*h)/3}}}


from right triangle,  slant height is hypotenuse, the radius and the height are legs


{{{r=sqrt(s^2-h^2)}}}


{{{r=sqrt((9r)^2-(12sqrt(5))^2)}}}


{{{r=sqrt(81r^2-144(5))}}}


{{{r=sqrt(81r^2-720)}}}.....square both sides


{{{r^2=81r^2-720}}}


{{{720=81r^2-r^2}}}


{{{720=80r^2}}}


{{{r^2=720/80}}}


{{{r^2=9}}}


{{{r=3}}}


=>slant height {{{s=9r=9*3=27 }}}


then

{{{V=(pi*3^2*12sqrt(5))/3}}}


{{{V=(pi*3^cross(2)*12sqrt(5))/cross(3)}}}


{{{V= pi*3*12sqrt(5)}}}


{{{V= pi*36sqrt(5)}}}-> exact solution


approximately:

{{{V= 252.89}}}