The formulas of the volume and surface area of silos of different shapes are presented along with online calculators.
Cylindrical Silo with Hemisphrical Top
Formulas for Volume and Surface Area of the Silo
Volume of Silo = Volume of Cylinder + Volume of Half Sphere
\[ \text{Volume} = \pi r^2 h + \frac{2}{3} \pi r^3 \]
Surface Area of Silo = Area of Cylinder + Area of Half Sphere
\[ \text{Area} = 2\pi r h + 2\pi r^2 \]
Calculator
Cylindrical Silo with a Conical Top
Formulas for Volume and Surface Area of the Silo
Volume of Silo = Volume of Cylinder + Volume of Top Cone
\[ \text{Volume} = \pi r^2 h + \frac{1}{3} \pi r^2 h_t^2\]
Surface Area of Silo = Area of Cylinder + Area of Lateral Surface of Top Cone
\[ \text{Area} = 2\pi r h + \pi r \sqrt{h_t^2 + r^2} \]
Calculator
Cylindrical Silo with a Conical Top and Bottom
Formulas for Volume and Surface Area of the Silo
Volume of Silo = Volume of Cylinder + Volume of Top Cone + Volume of Bottom Cone
\[ \text{Volume} = \pi r^2 h + \frac{1}{3} \pi r^2 h_t^2 + \frac{1}{3} \pi r^2 h_b^2\]
Surface Area of Silo = Area of Cylinder + Area of Lateral Surface of Top Cone + Area of Lateral Surface of Bottom Cone
\[ \text{Area} = 2\pi r h + \pi r \sqrt{h_t^2 + r^2} + \pi r \sqrt{h_b^2 + r^2} \]
