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?

Question

xishem · Answer

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:$$423.0gal$$

anonymous · Answer

oh wow thanks for the help. do you think you can help me with some more math problems

xishem · Answer

Post them, and I'll do my best.

anonymous · Answer

ok
Workers plan to apply a reflective coating of paint to one surface of an equilateral triangular shaped highway sign. How many square inches of coating need to be applied to the sign if one side of the triangle is 14 inches?

xishem · Answer

Go ahead and post them as new questions.