Volume and surface of a composite solid

How to use it

1. 1Name the pieces first and list which of their faces survive on the outside; the joining circle or rectangle is not one of them.
2. 2Where one piece sits on another, express every length through the shared dimension, usually the common radius.
3. 3A tent, a dome or a silo has no fabric or painted floor, so the base of the lowest piece is excluded too.

Step-by-step

1. 1
   $V_{\text{cone}}=\frac{1}{3}\pi (3{)}^2(4)=12\pi$

   Why: The pieces share the radius $3$ cm.

2. 2
   $V_{\text{hemisphere}}=\frac{2}{3}\pi (3{)}^3=18\pi$
3. 3
   $V=12\pi +18\pi =30\pi$ cm${}^3$

   Why: Volumes add even though the joining faces do not.