\[ V_{\text{cone}} = \frac{\pi}{3} H (br^2 + br \cdot tr + tr^2) \]

Where:

• H = height of the conical section
• br = bottom radius (bottom diameter / 2)
• tr = top radius (top diameter / 2)

\[ R_{\text{cut}} = br + \left(\frac{H_{\text{filled}}}{H}\right) H \left(\frac{tr - br}{H}\right) \]

\[ V_{\text{filled}} = \frac{\pi}{3} \left(\frac{H_{\text{filled}}}{H}\right) H \left(br^2 + br \cdot R_{\text{cut}} + R_{\text{cut}}^2\right) \]

Where:

• H_{\text{filled}} = filled height
• H = height of the conical section
• br = bottom radius (bottom diameter / 2)
• tr = top radius (top diameter / 2)