Calculating Sand Volume for a Cylindrical Containment Vessel

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SUMMARY

The discussion focuses on calculating the volume of sand required to fill a cylindrical containment vessel surrounding a spherical pressure vessel with a diameter of 10 meters. The correct approach involves calculating the volume of the cylinder and then subtracting the volume of the sphere from it to determine the volume of sand needed. The volume of the sphere is calculated using the formula \( V = \frac{4}{3} \pi r^3 \), while the volume of the cylinder is calculated using \( V = \pi r^2 h \), where the radius of the sphere is 5 meters. The final calculation reveals the amount of sand required for complete filling.

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  • Understanding of geometric volume calculations
  • Familiarity with the formulas for the volume of a sphere and a cylinder
  • Basic knowledge of mathematical operations involving subtraction
  • Concept of spatial relationships in three-dimensional geometry
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  • Study the formula for the volume of a sphere: \( V = \frac{4}{3} \pi r^3 \)
  • Learn the formula for the volume of a cylinder: \( V = \pi r^2 h \)
  • Explore practical applications of volume calculations in engineering contexts
  • Research methods for calculating material requirements for construction projects
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nathan12345
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A spherical pressure vessel with a diamter of 10 m is tightly enclosed in a cylindrical containment vessel with the sphere just touching on all 4 sides . Additional protective material (assume is sand ) is added to the cyclinder to provide additional support .How much sand is required so that all the space in the cylinder is filled ?
I am beginning a new course , and I am pretty new to the topic , but in my head I would calculate the volume of the sphere , and then the cylinder , and subtract the volume of the cylinder from the volume of the sphere ? .
 
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Right... but it's the other way around: subtract the volume of the cylinder from the volume of the sphere...
 
subtract the volume of the sphere from the volume of the cylinder

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