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BUY ANIMATIONS: personal/ teaching/ commercial. BUY THIS ANIMATION of surface area of a cylinder! |

The animation starts with a translucent cylinder of height **r** and capped by two ends of radius **r**. The circumference of the cylinder is **2 π r**. The wall of the cylinder opens up to form a rectangle whose length is the circumference of the cylinder and whose height is **h**. This gives the area of the cylinder wall as **2 π rh**. The two ends of the cylinder hinge backwards to demonstrate their two areas. Each circle has an area of **π r ^{2}** (see area of a circle animation) giving a total area of the two ends as

In the particular case of a cylinder whose height is the same as its diameter (i.e. the height is equal to **2 r** ) that cylinder will perfectly inscribe a sphere of radius r. The formula becomes:

surface area of cylinder = **π r ^{2} + π r^{2} + (2 π r x 2 r)** =

The area of the cylinder is **6 π r ^{2}** and that of its circumscribed sphere is

Try our circle and area calculator to derive various values from different starting points.

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