CK-12 Geometry-Concepts

11.8. Composite Solids http://www.ck12.org

Example B

Find the surface area of the following solid.

This solid is a cylinder with a hemisphere on top. Because it is one fluid solid, we would not include the bottom of
the hemisphere or the top of the cylinder because they are no longer on the surface of the solid. Below, “LA” stands
forlateral area.

SA=LAcylinder+LAhemis phere+Abase circle

=πrh+

1

2

4 πr^2 +πr^2

=π( 6 )( 13 )+ 2 π 62 +π 62

= 78 π+ 72 π+ 36 π

= 186 πin^2

Example C

Find the volume of the following solid.

To find the volume of this solid, we need the volume of a cylinder and the volume of the hemisphere.

Vcylinder=π 62 ( 13 ) = 78 π

Vhemis phere=

1

2

(

4

3

π 63

)

= 36 π

Vtotal= 78 π+ 36 π= 114 πin^3

Watch this video for help with the Examples above.