To find the surface area and volume of composite shapes, they must first be broken down into simpler component shapes. The surface areas and volumes of each component shape are then calculated separately and summed. For surface area, overlapping portions must be accounted for to avoid overcounting. Volumes simply add together the individual volumes. The example demonstrates finding the total volume and surface area of a shape composed of a cylinder atop a prism by calculating and summing their individual volumes and surface areas.

1. Composite Figures
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 it 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.