MHB Calculating Sand Volume for a Cylindrical Containment Vessel

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To calculate the sand volume required for a cylindrical containment vessel enclosing a spherical pressure vessel, first determine the volume of the cylinder and the sphere. The sphere has a diameter of 10 m, leading to a radius of 5 m, while the cylinder's dimensions must be established based on the sphere's size. The correct approach is to subtract the volume of the sphere from the volume of the cylinder to find the volume of sand needed. This calculation ensures that all space in the cylinder is filled with sand, providing the necessary support for the sphere. Accurate volume calculations are essential for effective containment and safety.
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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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Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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