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Hi all, stuck on a related rate problem that i could use some help with. Basically I need to find a formula for the change of height of the water level in a sphere that's being filled at a constant volume. Starting with an empty sphere (r = 1.25in) water is flowing into the sphere at a constant rate (dV/dt = 1.3635 in^3/sec) and I need to find the rate of change of the height of the water level (dh/dt) as it related to time. Struggling because when I differentiate the formula for a spherical cap, V = ((pi*h^2)/3)(3r-h), it becomes something that isn't very easy to work with. Unlike a cylinder, where the volume of liquid is also a cylinder, or a cube, where the fluid volume is also a prism, obviously a partially filled sphere is not a sphere. I think this is the source of my issues. Help would be appreciated! Thanks.
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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}
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