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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 5 years, 4 months ago

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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 $\displaystyle R$.

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Right.

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

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

need help fast

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

thanks 2 all

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

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## Comments

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TopNewestBy 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 $\displaystyle R$.

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Right.

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

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S = 2

pix ; x= R[1-h/H]Log in to reply

need help fast

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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

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thanks 2 all

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

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