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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, 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 $$\displaystyle R$$.

- 3 years, 8 months ago

Right.

- 3 years, 8 months ago

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

- 3 years, 8 months ago

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

- 3 years, 8 months ago

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

- 3 years, 8 months ago

thanks 2 all

- 3 years, 8 months ago

need help fast

- 3 years, 8 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

- 3 years, 8 months ago