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To understand the area of cylinder formula that works out the surface area of a cylinder.

The first thing to do is to think about how a cylinder shape comes together.

A cylinder has a pipe shape middle section, which is called the lateral surface. Along with having two bases, which are both circles, one on each end.

The cylinder itself has a height, and also a radius, which is the same as the radius of the two circle bases.

When the curved middle lateral surface is opened up and laid out flat, the shape of the surface actually becomes a rectangle.

The width of this rectangle, is the same as the distance around of both of the circles at the bases of the cylinder, their circumferences.

The circumference of
a circle is given by **π** multiplied by twice the radius. **2****π****r**

We can see that the surface area of the pipe shape lateral surface, is the same as the area when it’s laid out as a rectangle. Which is the width multiplied by the height.

**2****π****r** × **h** =>
**2****π****r****h**

While the two bases of the cylinder being circles that are the same size.

The *area* of one of
the circles is given by **π r**².

So the area of
both circle bases combined is double this, **2****π****r**².

Knowing all of this, it can now be seen that the entire surface area of a cylinder is put together like so.

Resulting in the full area of cylinder formula for the surface area:

**2****π****r**² +
**2****π****r****h**

__Examples__

__(1.1)__

What is the area of the following cylinder.

__(1.2)__

A section of an oil pipeline is in the shape of an open cylinder.

The section has the following dimensions.

What is the surface area of the section?

__Solution__

An open cylinder is a cylinder which has no bases. So it just contains the curved lateral surface.

Thus the area is
given only by **2****π****r****h**.

Area of pipeline section = **2****π** × **4** × **10** = **251.33**m²

Most of the time, when people mention the term cylinder, they mean a right cylinder.

Which is what we’ve seen so far on this page, where the two circle bases are parallel and lined up
with each other.

An oblique cylinder on the other hand, is a cylinder where the two circle bases are not aligned, but
they area still the same size as each other.

So as well as a perpendicular height, there is also a slope, or a slant height, in the cylinder
shape.

To work out the surface area of a cylinder in this situation, you need to use the slant-height
instead of the actual height straight up from the ground.

Which results in:

There is also another formula that can be used to find the surface area of an oblique cylinder.

The information required is the **radius**, the vertical **height**, and also the angle
that the oblique cylinder is tilted at, **θ**.

In this situation, the area of the oblique cylinder can be given by:

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