The student is able to find the surface area and volume of composite figures made up of simpler shapes. To solve such problems, one breaks the composite figure down into constituent shapes like prisms and cylinders and then calculates the surface area and volume of each shape individually before summing them. For surface area, one must account for any overlapping portions between shapes.

1. 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 cylinder
2
3
9 4 5 2 3
180 12 217.7 cm
V V V= +
= + π
= + π ≈

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