volume using cross-sections

Calculus
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a square of of side length s lies in a plane perpendicular to a line L. one vertex of the square lies on l. as this square moves a distance h along l, the square turns one revolution about l to generate a corkscrew-like column with square cross-section. find the volume of the column

May 15th, 2015

I considered an element of distance "dH", the corresponding element of angle "dx" must satisfy dx/dH = H/2pi hence dx = 2*pi*dH/h. As dH tends to zero, dx tends to zero, and the element of volume dV approximates to a cuboid of sides s, s and dH. Hence dV = (s^2)dH and V = (s^2)H by integration.

May 15th, 2015

so the volume will be s^2H

May 15th, 2015

what will be the volume be if the square turns twice instead of once

May 15th, 2015

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May 15th, 2015
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