What is the surface area of a slanted cylinder?

This is part of a series on common misconceptions.

Is this true or false?

A cylinder which has slant height \( l \) and circular flat surfaces with radius \( r \) has a total surface area equal to \( 2 \pi r (r + l ) \).

Why some people say it's true: The total surface area of a right cylinder is \( 2 \pi r (r + h ) \), where \( h \) is the height of the cylinder. The surface area of the slanted cylinder can be calculated in a similar way, using slanted height instead. Hence the surface area of a slanted cylinder is \( 2 \pi r (r + l ) \).

Why some people say it's false: (One-line explanation that a beginner might give)

The statement is \( \color{red}{\textbf{false}}\).

Proof:

(Complete proof of the statement)

Rebuttal: (Address any concerns that people have)
Reply: (Explain why the argument is not vald)

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Rebuttal:
Reply:

(If relevant, add in an example problem that demonstates understanding of this misconception.

See Also

• List of Common Misconceptions
• Surface Area