Water is stored in a hemispherical tank with a radius of 5m. When the tank is fi

Question

Water is stored in a hemispherical tank with a radius of 5m.

When the tank is filled to depth h, the water occupies a spherical cap. Show that the volume of this cap is V=pie h^2(3r-h)/3. Where r is the radius of the sphere and 0<h<r. The easiest way to do this calculation is to start with the circle x^2+y^2=r^2, identify the region R with height h, and revolve it around the y axis. Then use either the disk method or the shell method to find the volume of the resulting solid.

Graph the volume function V=f(h) in part (a) with r=f for 0<h<5. Check that the function has the expected properties; for example f(0)= 0 and f(5) is the volume of the entire hemisphere.

How much water is in the tank if it is filled to a depth of h=3.5 meters?

Water is stored in a hemispherical tank with a radius of 5m. When the tank is filled to depth h, the water occupies a spherical cap. Show that the volume of this cap is V=pie h^2(3r-h)/3. Where r is the radius of the sphere and 0

Explanation / Answer

When depth is h, volume in cap = V = pi*h

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