cylinder volume

[toki]

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

[mathematic]

Thin circular strip at distance r from center has area [latex]2\pi rdr[/latex].

[Sensei]

[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.

 

 

[toki]

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

[Fuzzwood]

Then you probably have a calculus book covering the chapter of integration?

[swansont]

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?

[mathematic]

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.

[studiot]

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

[toki]

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