CK-12 Geometry Concepts

http://www.ck12.org Chapter 11. Surface Area and Volume

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.

MEDIA

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CK-12 Foundation: Chapter11CompositeSolidsB

Vocabulary

Acomposite solidis a solid that is composed, or made up of, two or more solids.Surface areais a two-dimensional
measurement that is the total area of all surfaces that bound a solid.Volumeis a three-dimensional measurement
that is a measure of how much three-dimensional space a solid occupies.

Guided Practice

1. Find the volume of the composite solid. All bases are squares.


2. Find the volume of the base prism. Round your answer to the nearest hundredth.