The Surface Area of a Cylinder
Eplained Step by Step

The Surface Area of a Cylinder is one of two major areas of the cylinder that your K-6 student must master.  The other is the volume of a cylinder, which I deal with on a different page.

To have any success in this area, your child must have a firm understanding of what area is.  If this is not the case, I highly recommend you stop, and work on that first.

Otherwise your child is just going to get very confused.  Your student must also understand the circle  and of cours the digits of Pi.

Surface area of a Cylinder

What is Surface Area?

The surface area of any figure, is the flat surface of all the shapes that combine to make the three dimensional object.  

So to make a cylinder you need a large rectangular shape, whose length is the same as the circumference of the two circles that close the cylinder at each end, and it's height, is the height of the cylinder it makes.

We all know that an image is worth a thousand words, so take a look at the image to the left.  

This is also called a 'net'.  (what a 3D-shape looks like when it is opened out flat.)

We can clearly see two circles and a rectangle.

So if the surface area of a cylinder is the combined areas of all the shapes that make the cylinder' then it must be the area of:

circle 1 + area of circle 2 + area of the rectangle.

Taking a Cylinder of Height h and Radius r:

Surface area of Cylinder = Area of top circle + Area of bottom circle + Area of Rectangle.

We know the two circles are the same size (must be to be a cylinder)

Surface area of Cylinder = 2 x (Area of circle) + Area of Rectangle.

Area of circle = Pi r2

We know from our Cylinder Net, that the length of the rectangle is the circumference of the circle: 2 Pi r

We also know the height of the rectangle is the height of the cylinder - h.

Area of Rectangle = (2 Pi r) x h

Surface Area of Cylinder = 2 x (Pi r2) + (2 Pi r) x h
Cylinders Surface Area = 2Pir2 + 2Pirh

Don't forget that once the concept is grasped, its on to practicing!  You can get all the worksheets you need to practice this new skill in our printable geometry worksheets.

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