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Volume of the rotating body , when a circle is rotated with respect to the x axis

ÀÛ¼ºÀÚ Uploader : ¹Ö±âÀû ÀÛ¼ºÀÏ Upload Date: 2019-01-14º¯°æÀÏ Update Date: 2019-01-15Á¶È¸¼ö View : 366

As shown in the figure, the volume V of the rotating body made by rotating a circle with respect to the x axis can be calculated as follows, if the circle has a radius of 'r' with its center located at a distance of 'a' from the x-axis.

x^2 + (y-a)^2 = r^2

y = a ¡¾(r^2 - x^2)^(1/2)

Upper semicircle : y = a + (r^2 - x^2)^(1/2) Lower semicircle : y = a - (r^2 - x^2)^(1/2)

Subtracting the volume made by which rotating the lower semicircle from the volume made by rotating the upper semicircle, we obtain the volume in question.

The integration interval is from -r to r.


*** Âü°í¹®Çå[References] ***

V = 2*a*¥ð^2*r^2
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