To find the surface area and volume of composite shapes, break them down into simpler component shapes and combine their individual areas and volumes. When calculating surface area, account for any portions of shapes that may be overlapped or covered by other shapes. Volumes simply add together while surface areas require considering both visible surfaces and any surfaces that may be obscured by other components.

1. 5.13.6 Composite Shapes
The student is able to (I can):
• Find the surface area and volume of composite figures

2. Much like composite plane figures, to find
the surface area and volume of composite
shapes, break them down into simpler
shapes and combine.
While volume is a fairly straightfoward
process, when you calculate the surface
area of a composite shape, you need to
take into account portions of the shape
that might be covered up by other shapes.

3. Example Find the volume and surface area of the
shape below.
Volume: total prism cylinderV V V= +
( )( )( ) ( )( )2
9 4 5 2 3= + π
3
180 12 217.7 cm= + π ≈

4. Example Find the volume and surface area of the
shape below.
Surface Area:
total prism cylS S L= +
( ) ( ) ( )[ ] ( )( )prismS 5 2 9 2 4 2 9 4
202
= + +
=
( )( )cylL 2 2 3
12
= π
= π
2
totalS 202 12 239.7 cm= + π ≈
We only need lateral area
because the one visible base
of the cylinder offsets the
missing circle on the prism.