CK-12 Geometry-Concepts

11.4. Cylinders http://www.ck12.org

If an oblique cylinder has the same base area and height as another cylinder, then it will have the same volume. This
is due to Cavalieri’s Principle, which states that if two solids have the same height and the same cross-sectional area
at every level, then they will have the same volume.

Example A

Find the surface area of the cylinder.

r=4 andh=12. Plug these into the formula.

SA= 2 π( 4 )^2 + 2 π( 4 )( 12 )

= 32 π+ 96 π

= 128 π

Example B

The circumference of the base of a cylinder is 16πand the height is 21. Find the surface area of the cylinder.

If the circumference of the base is 16π, then we can solve for the radius.

2 πr= 16 π

r= 8

Now, we can find the surface area.

SA= 2 π( 8 )^2 +( 16 π)( 21 )

= 128 π+ 336 π

= 464 π

Example C

Find the volume of the cylinder.