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### Surface Area of a Cylinder

```
Date: 11/22/97 at 17:28:09
From: John Daly
Subject: Geometry surface area formula

I need to find the surface area of a cylinder and the only formula
that I have is the lateral (unrolled) surface area:  2*pi*r*h .
Is there any difference between this formula and the regular surface
area formula for a cylinder?
```

```
Date: 11/26/97 at 11:17:27
From: Doctor Lim
Subject: Re: Geometry surface area formula

Hi there,

A cylinder can be open at both ends; when this is the case, the
formula for the surface area of the cylinder is 2*pi*r*h. This is
because the cylinder when cut up becomes a rectangle. The height of
the cylinder is the same as the height of the rectanble, while the
length of the rectangle is actually the circumference of the base of
the cylinder.

In the case of a cylinder with a base but no top, the surface area
becomes the total surface area of the cylinder with the base (but
with no top), which equals:

the rectangular area of the wall of the cylinder
plus the circular area of the base.

= 2*pi*r*h + (pi)r^2

In the case of the cylinder with a base and a cover at the top, the
surface area of this cylinder becomes the total surface area of the
cylinder (with base and cover at the top), which equals:

the rectangular area of the wall of the cylinder
plus the circular area of the base.
plus the circular area of the cover at the top

= 2*pi*r*h + (pi)r^2 + (pi)r^2
= 2*pi*r(r + h)

So in the calculation of the surface area, we have to be careful to
add the surface areas of the different parts of the solid. Got the
idea?

Happy calculating!

Doctor Lim,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Geometry
Middle School Higher-Dimensional Geometry

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