cylinder....... help

A circular cylinder is inscribed in a given cone of radius R cm and height H cm as shown in the figure Find the curved surface area S of the circular cylinder as a function of x Find the relation connecting x and R when S is maximum

#HelpMe! #Pleasehelp

Easy Math Editor

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Comments

By Similarity of Triangles,
$\displaystyle \frac{h}{R-x} = \frac{H}{R}$

$\displaystyle\Rightarrow h = \frac{H}{R} (R-x)$

Now, it is clear that,
$\displaystyle S = 2\pi x\times h$

Substitute the value of $\displaystyle h$ and get $\displaystyle S$ as a function of $\displaystyle x$ .

Differentiate the function that you just derived wrt $\displaystyle x$ , and put it equal to $\displaystyle 0$ .

You will find a relation between $\displaystyle x$ and $\displaystyle R$ .

Anish Puthuraya - 7 years, 4 months ago

Right.

Soham Dibyachintan - 7 years, 4 months ago

2pixh = S, x = R(1-h/H)..............................................................(when S is maximum)

Hrishikesh Dani - 7 years, 4 months ago

S = 2pix ; x= R[1-h/H]

Gaurav Chaudhary - 7 years, 4 months ago

need help fast

Sonali Sukesh - 7 years, 4 months ago

put H/R =k k=(H-h)/x from this h=H-kx after this S=2pixh put h=H-kx differentiate with respect to x and put dS/dx=0 from this x=R/2

Rohit Dogra - 7 years, 4 months ago

thanks 2 all

Sonali Sukesh - 7 years, 4 months ago

right 2pixh = S, x = R(1-h/H)..........(when S is maximum)

Harsh Shah - 7 years, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$