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# Why is the area of sphere the same with volume of cylinder?

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Why is the surface area of sphere the same with volume of cylinder?

surface area of sphere = 4*ㅠ*r^2

volume of cylinder = ㅠ*r^2*h

Dec 8, 2014

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flflvm97......I think you're getting something confused......

The surface area of a sphere has the same surface area as that of a cylinder with the same radius as the sphere and a height = the diameter of the sphere = 2r  ...  thus  .....

Csa = (2*pi*r *h)  = 2*pi*r * (2r) =  4 * pi * r^2

Dec 9, 2014

#1
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These are not the same.

A cylinder is a prism and the volume of any prism is the area of the cross section times by the height (or depth as I often prefer to call it)

The cross section of a cylinder is a circle and its area is   $$A=\pi r^2$$

So  the volume of the prism is     $$V=\pi r^2h\quad units ^3$$

Now I could probably only give a calculus reason as to why the SA of a sphere is   $$SA=4\pi r^2\quad unit^2$$

But anyway they are  not the same.

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I know you gave a calculus answer for another question.  Did you actually understand it or did you copy it.

I don't mind either way - it was a great answer.  I am just trying to assess your level.

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Dec 9, 2014
#2
+114442
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