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How does pressure change in a combustion engine? How fast does the water level rise when filling a pool? Calculus quantifies the impact of change on areas, angles, distances, temperatures, and more.

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A spherical fish tank of radius 10 meters is being filled with at a constant rate of \(R\pi\) cubic meters of water per second. At height 6 meters, the rate of change of the height is 1 meter per second. What is the value of \(R\)?

**Details and assumptions**

The height is measured from the bottom of the sphere (i.e. in contact with the ground).

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