Related Rates of Change Question

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Homework Statement

A spherical tank with an interior diameter of 2m is being filled with water at a rate of 10 liters per second. Determine what rate the height of the water is increasing at when the tank is half full.

Homework Equations

[tex] V=\frac{2\pi r^3}{3}-\pi r^2d+\frac{\pi d^3}{3}[/tex]

Where r is the radius of the sphere and d is the distance from the surface of the water to the top of the hemisphere.

The Attempt at a Solution

We want to find [tex]\frac{dh}{dt}[/tex] but we need another variable to use the chain rule. So I suppose we need to use [tex]\frac{dh}{dt}=\frac{dh}{dV}X\frac{dV}{dt}[/tex]
as we've got the rate of volume fill per second (10 liters per second). So how would I go about making h in terms of v?

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  • #2

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