toki Posted December 8, 2015 Share Posted December 8, 2015 for a dv volume cylinder we get dv=2*pi*r*dr*L but why to multiply this r with dr.please make it understand Link to comment Share on other sites More sharing options...
mathematic Posted December 9, 2015 Share Posted December 9, 2015 Thin circular strip at distance r from center has area [latex]2\pi rdr[/latex]. Link to comment Share on other sites More sharing options...
Sensei Posted December 9, 2015 Share Posted December 9, 2015 [math]A=\pi*r^2[/math] is area of base in m2 If you will multiply it by height: [math]V=\pi*r^2*h[/math] you will get volume in m3. Notice that you can have other shape as base, f.e. square [math]A=r^2[/math] Once it's multiplied by height you get: [math]V=r^2*h[/math] If h=r, it simplifies to: [math]V=r^3[/math] and you have volume of a box with all sides equal length. Link to comment Share on other sites More sharing options...
toki Posted December 9, 2015 Author Share Posted December 9, 2015 but how Thin circular strip at distance r from center has area 2\pi rdr. I don't know. I'm new high school student Link to comment Share on other sites More sharing options...
Fuzzwood Posted December 9, 2015 Share Posted December 9, 2015 Then you probably have a calculus book covering the chapter of integration? Link to comment Share on other sites More sharing options...
swansont Posted December 9, 2015 Share Posted December 9, 2015 but how Thin circular strip at distance r from center has area 2\pi rdr. I don't know. I'm new high school student How would you find the area of a circular strip of finite size? Link to comment Share on other sites More sharing options...
mathematic Posted December 10, 2015 Share Posted December 10, 2015 but how Thin circular strip at distance r from center has area 2\pi rdr. I don't know. I'm new high school student Circumference of circle is [latex]2\pi r[/latex]. Thickness of infinitesimal strip is dr. Link to comment Share on other sites More sharing options...
studiot Posted December 10, 2015 Share Posted December 10, 2015 (edited) You say you are a new high school student. Did you miss a term or some lessons? Has your class already started differentiation? The formula for the volume of a cylinder is [math]V = \pi {r^2}L[/math] Differentiate with respect to r [math]\frac{{dV}}{{dr}} = 2\pi rL[/math] Rearrange to obtain your formula [math]dV = 2\pi rLdr[/math] Does any of this mean anything to you? Edited December 10, 2015 by studiot 1 Link to comment Share on other sites More sharing options...
toki Posted December 10, 2015 Author Share Posted December 10, 2015 actually I'm from Bangladesh ♥ our curriculum does not cover calculas in high school level. in college level we learn it. and tnx all. iv understood Link to comment Share on other sites More sharing options...
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