Question 1208875: A bowl with radius 30 cm , shaped like a hemisphere, is filled with water to two-thirds its depth. What is the surface area of the water, in cm²?
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
A bowl with radius 30 cm , shaped like a hemisphere, is filled with water
to two-thirds its depth. What is the surface area of the water, in cm²?
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The total depth of the bowl is the radius of 30 cm (given).
Two-thirds of the total depth is 2/3 of 30 cm, i.e. 20 cm.
Hence, 10 cm is over the water surface.
Thus the square of the radius of the water surface in the bowl is (from Pythagoras)
r^2 = 30^2 - 10^2 = 900 - 100 = 800 cm^2
Hence, the surface area of the water in the bowl is
 =  = 2513.27412 cm^2, or 2513.27 cm^2 (rounded). ANSWER
Solved.
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