Volume of Silo bin with Cone top

[zeshkani1985]

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 or equal to the height of the conical section, hcone.
V=1/3r_h²h if h ≤ h_cone
and rh is the radius at height h: r_h=tan∅ if r_h ≤ R.

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=1/3∏r²h_cone+∏r²(h-h_cone) if h > h_cone.
If the height of the conical section is 3.0 m, the radius of the cylindrical section is 2.0 m, and the total height of the storage bin is 10.0 m, what is the maximum volume of material that can be stored?

here is what i did. I found the volume of the cone since it says we are given a conical height of 3 and the radius of 2 so i get a volume of about 12m³ and I get the cylinidrical volume by just V=∏r²h since were are given the total height of the bin at 10m so the cylinder must be 7m tall since (10-3h_cone=7) and the volume of the cylinder is about 87m³ so the total volume is them combined to give me a total volume of around V=100m³

is this right?

 

[Astronuc]

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 or equal to the height of the conical section, hcone.
V=1/3r_h²h if h ≤ h_cone
and rh is the radius at height h: r_h=tan∅ if r_h ≤ R.

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=1/3∏r²h_cone+∏r²(h-h_cone) if h > h_cone.
If the height of the conical section is 3.0 m, the radius of the cylindrical section is 2.0 m, and the total height of the storage bin is 10.0 m, what is the maximum volume of material that can be stored?

here is what i did. I found the volume of the cone since it says we are given a conical height of 3 and the radius of 2 so i get a volume of about 12m³ and I get the cylinidrical volume by just V=∏r²h since were are given the total height of the bin at 10m so the cylinder must be 7m tall since (10-3h_cone=7) and the volume of the cylinder is about 87m³ so the total volume is them combined to give me a total volume of around V=100m³

is this right?

The formula V=1/3∏r²h_cone+∏r²(h-h_cone) is correct. So one is looking for the total volume subject to the constraint of the given dimensions.