how to find the lateral side surface of the area of a cone... segment y=1/4x from x=0 to x=9 about the x-axis.

Question

anonymous · Answer

liket his ?
|dw:1402479666392:dw|

anonymous · Answer

|dw:1402479838982:dw|

anonymous · Answer

Yes!

anonymous · Answer

wanna use geometry or calcules ?

anonymous · Answer

Calc

anonymous · Answer

use  the formula for the area of a surface of revolution obtained by rotating the graph curve about the x-axis ,, do u have it ?

anonymous · Answer

in ur tt book ?

anonymous · Answer

i guess around y its
$\large 2\pi \int_a^b x.\sqrt {1+f'(x)^2  } dx $

we should make it around y  T_T

anonymous · Answer

wait i ment we need it around x..

anonymous · Answer

Mhmm!

anonymous · Answer

So far I have most of it filled in, I'm just missing the dy/dx

anonymous · Answer

The y=1/4x ?

anonymous · Answer

And, the dy/dx = 1/2rootx ?

ganeshie8 · Answer

$$\large  SA =  \int  \limits_0^9 2\pi y  ~ ds =  \int  \limits_0^9 2\pi \left(\frac{1}{4}x\right) \sqrt{1 + \left(\dfrac{dy}{dx}\right)^2} ~dx$$

ganeshie8 · Answer

$\large y = \dfrac{1}{4}x  \implies  \dfrac{dy}{dx} = ?$