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 'erroneously finding discrepancy in transpose rule'

Thread 'erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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