1. Tardigrade
  2. Question
  3. Mathematics
  4. The radius of a right circular cylinder of greatest curved surface which can be inscribed in a given right circular cone is:

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The radius of a right circular cylinder of greatest curved surface which can be inscribed in a given right circular cone is:

Application of Derivatives

Solution:

$\frac{ H }{ R }=\frac{ H - h }{ r }$
$S =2 \pi rh$
$=2 \pi H \left( r -\frac{ r ^2}{ R }\right)$
$\frac{ dS }{ dr }=2 \pi H \left(1-\frac{2 r }{ R }\right)$
image
Maximum at $r=\frac{R}{2}$