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A fairly common shape for a dry-solids storage bin is a cylindrical silo with a conical collecting section at the base where the product is removed (see Figure 4.60.) Figure 4.60 Storage silo. To calculate the volume of the contents, you use the formula for a cone, as long as the height of product, h, is less than the height of the conical section, hoone (4.11) Here, It is the radius at height hand can be calculated from h by using trigonometry: (4.12) V = ²h ifh hoone- If the height of the conical section is 3 meters, the radius of the cylindrical section is 2 m, and the total height of the storage bin is 10 meters, what is the maximum volume of material that can be stored?

A fairly common shape for a dry-solids storage bin is a cylindrical silo with a conical collecting section at the base where the product is removed (see Figure 4.60.) Figure 4.60 Storage silo. To calculate the volume of the contents, you use the formula for a cone, as long as the height of product, h, is less than the height of the conical section, hoone (4.11) Here, It is the radius at height hand can be calculated from h by using trigonometry: (4.12) V = ²h ifh hoone- If the height of the conical section is 3 meters, the radius of the cylindrical section is 2 m, and the total height of the storage bin is 10 meters, what is the maximum volume of material that can be stored?

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Finding the Volume of a Storage Bin I

### Volume Calculation for a Cylindrical Silo with a Conical Base A fairly common shape for a dry-solids storage bin is a cylindrical silo with a conical collecting section at the base where the product is removed (see Figure 4.60). #### Diagram Description **Figure 4.60:** Storage silo. - The diagram depicts a cylindrical silo with a conical base. - \( h_{\text{cone}} \) is the height of the conical section. - \( \theta \) is the angle of the cone. - \( R \) is the radius at the base of the cylindrical section. #### Volume Calculation To calculate the volume of the contents, you use the formula for a cone, as long as the height of the product, \( h \), is less than the height of the conical section, \( h_{\text{cone}} \). \[ V = \frac{1}{3} \pi {r_h}^2 h \quad \text{if} \quad h < h_{\text{cone}} \] (Equation 4.11) Here, \( r_h \) is the radius at height \( h \) and can be calculated from \( h \) using trigonometry: \[ r_h = h_{\text{cone}} \tan(\theta) \] (Equation 4.12) If the height of the stored product is greater than the height of the conical section, the equation for a cylinder must be added to the volume of the cone: \[ V = \frac{1}{3} \pi R^2 h_{\text{cone}} + \pi R^2 (h - h_{\text{cone}}) \quad \text{if} \quad h > h_{\text{cone}} \] (Equation 4.13) If the height of the conical section is 3 meters, the radius of the cylindrical section is 2 meters, and the total height of the storage bin is 10 meters, what is the maximum volume of material that can be stored?
Transcribed Image Text:### Volume Calculation for a Cylindrical Silo with a Conical Base A fairly common shape for a dry-solids storage bin is a cylindrical silo with a conical collecting section at the base where the product is removed (see Figure 4.60). #### Diagram Description **Figure 4.60:** Storage silo. - The diagram depicts a cylindrical silo with a conical base. - \( h_{\text{cone}} \) is the height of the conical section. - \( \theta \) is the angle of the cone. - \( R \) is the radius at the base of the cylindrical section. #### Volume Calculation To calculate the volume of the contents, you use the formula for a cone, as long as the height of the product, \( h \), is less than the height of the conical section, \( h_{\text{cone}} \). \[ V = \frac{1}{3} \pi {r_h}^2 h \quad \text{if} \quad h < h_{\text{cone}} \] (Equation 4.11) Here, \( r_h \) is the radius at height \( h \) and can be calculated from \( h \) using trigonometry: \[ r_h = h_{\text{cone}} \tan(\theta) \] (Equation 4.12) If the height of the stored product is greater than the height of the conical section, the equation for a cylinder must be added to the volume of the cone: \[ V = \frac{1}{3} \pi R^2 h_{\text{cone}} + \pi R^2 (h - h_{\text{cone}}) \quad \text{if} \quad h > h_{\text{cone}} \] (Equation 4.13) If the height of the conical section is 3 meters, the radius of the cylindrical section is 2 meters, and the total height of the storage bin is 10 meters, what is the maximum volume of material that can be stored?
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