Look at the picture.
The formula of the volume of a cylinder:
[tex]V_C=\pi r^2H[/tex]
We have:
[tex]d=6m;\ d=2r\to r=3m\\H=25m[/tex]
Substitute:
[tex]V_C=\pi\cdot3^2\cdot25=225\pi\ m^3[/tex]
The formula of the volume of a sphere:
[tex]V_S=\dfrac{4}{3}\pi r^3[/tex]
We have a hemisphere, therefore the formula of the volume is:
[tex]V_H=\dfrac{1}{2}V_S=\dfrac{1}{2}\cdot\dfrac{4}{3}\pi r^3=\dfrac{2}{3}\pi r^3[/tex]
We have:
[tex]r=3m[/tex]
Substitute:
[tex]V_H=\dfrac{2}{3}\pi\cdot3^3=\dfrac{2}{3}\pi\cdot27=2\pi\cdot9=18\pi\ m^3[/tex]
The volume of a silo:
[tex]V=V_C+V_H\to V=225\pi+18\pi=243\pi\ m^3\approx243\cdot3.14\approx763\ m^3[/tex]
Answer: 763 m³.
