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# 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
3 years, 1 month 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 $$\displaystyle R$$. · 3 years, 1 month ago

Right. · 3 years, 1 month ago

2pixh = S, x = R(1-h/H)..............................................................(when S is maximum) · 3 years, 1 month ago

S = 2pix ; x= R[1-h/H] · 3 years, 1 month ago

right 2pixh = S, x = R(1-h/H)..........(when S is maximum) · 3 years, 1 month ago

thanks 2 all · 3 years, 1 month ago

need help fast · 3 years, 1 month ago