# 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 Note by Sonali Sukesh
6 years, 9 months ago

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

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

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 $\displaystyle R$.

- 6 years, 9 months ago

Right.

- 6 years, 9 months ago

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

- 6 years, 9 months ago

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

- 6 years, 9 months ago

need help fast

- 6 years, 9 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

- 6 years, 9 months ago

thanks 2 all

- 6 years, 9 months ago

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

- 6 years, 9 months ago