Surface Area of Composite Solids
Maths: Edexcel GCSE Higher, topic 4.10.5
Surface Area of Composite Solids
What is a composite solid?
A composite solid is made by joining two or more simple 3D shapes together.
To find the total surface area, we only calculate the area of the faces on the outside.
The Hidden Face Rule
When two shapes are glued together, their touching faces become hidden inside.
These hidden faces do not count towards the total surface area.
Remember to subtract the overlapping area from your final calculation.
Cylinder on a Cuboid
Imagine a circular cylinder standing on a rectangular box.
The top of the box is not a full rectangle anymore; it has a circular footprint covering it.
Calculate the full box, full cylinder, and subtract the circular base 2 times (once from each shape).
Hollow Solids
If a composite shape has a hole drilled through it, the total surface area changes.
You must subtract the shape of the hole from the outside faces.
But you must add the new surface area of the inside walls.