The cost of painting the total surface area of cone at 25 paise per cm2 is Rs 176. Find the volume of the cone, if its slant height is 25cm.
Total surface area of cone =πrl+πr2
where l is the slant height & r is radius
TSA of cone =total costcost/cm2=1760.25=704cm2
So πrl+πr2=704
⇒πr[l+r]=704
⇒227r[25+r]=704
⇒r2+25r−224=0
⇒(r+32)(r−7)=0
⇒r=7,−32 [radius cannot be negative]
⇒r=7
volume of cone =13πr2√l2−r2
=13×227×7×7×√252−72
=1231.504