Surface area of a cylinder
The number of square units it takes to exactly cover the surface of a cylinder.
Drag the orange dot to the left to "unroll" the cylinder.
How to find the surface area of a cylinder
The surface area of a cylinder can be found by breaking it down into three parts:
- The two circles that make up the ends of the cylinder.
- The side of the cylinder, which when "unrolled" is a rectangle
In the figure above, drag the orange dot to the left as far as it will go.
You can see that the cylinder is made up of two circular disks and a rectangle that is like the label unrolled off a soup can.
The area of each end disk can be found from the
radius r of the circle.
The area of a circle is πr2,
so the combined area of the two disks is twice that, or2πr2.
(See Area of a circle).
The area of the rectangle is the width times height.
The width is the height h of the cylinder, and the length is the distance around the end circles.
This is the
circumference of the circle
and is 2πr. Thus the rectangle's area is 2πr × h.
Formula for the surface area of a cylinder
Combining these parts we get the final formula:
π is Pi, approximately 3.142
r is the radius of the cylinder
h height of the cylinder
By factoring 2πr from each term we can simplify this to
However, the first is the one shown in most textbooks and more clearly shows how it is derived.
Remember that the radius and the height must be in the same units - convert them if necessary. The resulting area will be in those square units.
So, for example if the height and radius are both in centimeters, then the area will be in square centimeters.
Things to try
In the figure above, adjust the height and diameter of the cylinder and note how the surface area is calculated.
Click 'reset' and 'hide details'. Adjust the cylinder to a new size and calculate the surface area. Click 'show details' to verify your answer.
Click 'reset'. Calculate what happens if you double the height - does the surface area double also?
Click 'reset'. Calculate what happens if you double the diameter - does the surface area double also?
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