Answer:
See explanation
Step-by-step explanation:
The combined shape consists of two hemispheres with radius of 2 mm and a circular cylinder with base radius of 2 mm and height of 10 mm.
Find the volume for each individual shape:
[tex]V_{hemisphere}=\dfrac{1}{2}\cdot \dfrac{4}{3}\cdot \pi r^3=\dfrac{2}{3}\cdot \pi\cdot 2^3=\dfrac{16}{3}\pi \ mm^3[/tex]
[tex]V_{cylinder}=\pi r^2h=\pi \cdot 2^2\cdot 10=40\pi \ mm^3[/tex]
Find the composite volume of the original figure:
[tex]V{combined \ figure}=\\ \\=2V_{hemisphere}+V_{cylinder}=\\ \\=2\cdot \dfrac{16}{3}\pi +40\pi =\\ \\=\dfrac{32}{3}\pi +40\pi =\\ \\=\dfrac{152}{3}\pi \ mm^3[/tex]
