Concept 12.1
Surface Area of a Combined Solid
Source: NCERT Mathematics, Class 1010 minute lesson
Formal statement
The surface area of a solid made by joining two solids is the sum of the curved and flat surfaces that remain exposed. Faces that are joined together are not part of the surface.
The intuition
Think of painting the solid. For a toy made of a cone on a hemisphere, you paint the cone's curved surface and the hemisphere's curved surface. The circle where they join is hidden inside.
So total surface areas don't simply add. You add only the pieces you could actually touch.
The attention
Look at which surfaces are still exposed after joining.
Toy = CSA of cone + CSA of hemisphere not TSA cone + TSA hemisphere
Look hereNot here
- Look here
- The surfaces still exposed. Only surfaces on the outside count. The circular faces where the two solids meet are covered.
- Not here
- Whole total surface areas added. Adding total surface areas includes the joining faces, which nobody could paint.
- What it teaches
- Before adding parts, ask what disappears when they combine.