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

Question

The radius of a right circular cylinder of greatest curved surface which can be inscribed in a given right circular cone is: (A) one third that of the cone (B) 1 / √2 times that of the cone (C) 2 / 3 that of the cone (D) 1 / 2 that of the cone

Tardigrade Admin · Accepted Answer

( H / R )=( H - h / r ) S =2 π rh =2 π H ( r -( r 2/ R )) ( dS / dr )=2 π H (1-(2 r / R )) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/8ca92dbb9e636fc72c2f4609e1ae8718-.png" /> Maximum at r=(R/2)

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

one third that of the cone

$1/ 2$ times that of the cone

$2/3$ that of the cone

$1/2$ that of the cone

$\frac{H}{R} = \frac{H - h}{r}$
$S = 2 π r h$
$= 2 π H (r - \frac{r ^{2}}{R})$
$\frac{d S}{d r} = 2 π H (1 - \frac{2 r}{R})$

Maximum at $r = \frac{R}{2}$

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

one third that of the cone

1/2​ times that of the cone

2/3 that of the cone

1/2 that of the cone

RH​=rH−h​ S=2πrh =2πH(r−Rr2​) drdS​=2πH(1−R2r​) Maximum at r=2R​

$1/ 2$ times that of the cone

$2/3$ that of the cone

$1/2$ that of the cone

$\frac{H}{R} = \frac{H - h}{r}$
$S = 2 π r h$
$= 2 π H (r - \frac{r ^{2}}{R})$
$\frac{d S}{d r} = 2 π H (1 - \frac{2 r}{R})$

Maximum at $r = \frac{R}{2}$