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=?h?(3r-h)/3.  Where r id the radius of the sphere and 0?h?r.  The easiest way t do this calculation is t start with the circle x?+y?=r?, 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=?h?(3r-h)/3. Where r id the radius of the sphere and 0?h?r. The easiest way t do this calculation is t start with the circle x?+y?=r?, 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. the circle x?+y?=r?, 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?

Explanation / Answer

(a) When depth is h, volume in cap = V = ?h

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