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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 4 years, 8 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]

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

thanks 2 all

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

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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

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

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thanks 2 all

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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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