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
5 years, 8 months ago

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

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

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

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

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

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

Anish Puthuraya - 5 years, 8 months ago

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Right.

Soham Dibyachintan - 5 years, 8 months ago

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

Hrishikesh Dani - 5 years, 8 months ago

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

Gaurav Chaudhary - 5 years, 8 months ago

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need help fast

Sonali Sukesh - 5 years, 8 months ago

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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

Rohit Dogra - 5 years, 8 months ago

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thanks 2 all

Sonali Sukesh - 5 years, 8 months ago

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

Harsh Shah - 5 years, 8 months ago

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