SOLUTION: A bowl is in the shape of a hemisphere (half sphere) with radius 10 cm. The surface of the water in the container has a radius of 7 cm. How deep is the water? Give your answer to

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Question 1195509: A bowl is in the shape of a hemisphere (half sphere) with radius 10 cm. The surface of the water in the
container has a radius of 7 cm. How deep is the water? Give your answer to one decimal place.

Found 2 solutions by bushra444, math_helper:
Answer by bushra444(1) About Me  (Show Source):
You can put this solution on YOUR website!
The distance from the hemisphere center to the water surface in the bowl is (Pithagoras)
\sqrt{10^2-7^2}=\sqrt{100-49}=\sqrt{51}
Then the depth of the water in the bowl is

10-\sqrt{51} = 2.9 cm (to one decimal place).

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!

A 'gas tank' type problem...
The bowl has the shape +y+=+-sqrt%28100-x%5E2%29+ and we can add 10 to get
the bottom of the bowl to sit exactly at the origin +y+=+10-sqrt%28100-x%5E2%29+.
So for water with radius 7: +y+=+-sqrt%28100-7%5E2%29+%2B+10+=+-sqrt%2851%29%2B10+
which is approx 2.85857.
The height, h (green line), to one decimal place is therefore +highlight%282.9cm%29+
+graph%28400%2C400%2C-12%2C12%2C-12%2C12%2C+y=-sqrt%28100-x%5E2%29%2B10%2C+y=2.9+%29+