A designer wants to make use of a half-spherical cistern in a water system. If the cistern has a diameter of 6 feet, how many gallons of water can it hold?

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A designer wants to make use of a half-spherical cistern in a water system. If the cistern has a diameter of 6 feet, how many gallons of water can it hold?

Mathematics
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The volume of a sphere is defined as\[V=\frac{4}{3}\pi r^3\]A semi-sphere would have half the volume of a sphere with the same diameter: \[V=\frac{2}{3}\pi r^3\]Also,\[r=D/2\]So, \[V=\frac{2}{3}(\pi)(D/2)^3=\frac{2}{3}(\pi)(6ft/2)^3=\frac{2}{3}\pi 27ft^3=56.55ft^3\]\[56.55ft^3*\frac{7.48051948gal}{1ft^3}=423.01gal\]We are only justified in keeping one significant figure, but it depends on what course this is for. If sigfigs matter: \[400gal\]If not, this is probably sufficient:\[423.0gal\]
oh wow thanks for the help. do you think you can help me with some more math problems
Post them, and I'll do my best.

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