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water is flowing through a pipe with radius 14 cm.The maximum depth of the water is 9 cm.
What is the width, PQ, of the surface of the water?
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The solution by @math_tutor2020 is INCORRECT.
The error is in incorrect using the intersecting chords theorem.
I came to bring a correct solution.
My solution is in two different forms, for better clarity.
Solution 1
In the post by math_tutor2020, you can see the right-angled triangle
with the hypotenuse of 14 cm (the radius from the center to the point P or Q)
and one leg of 14-9 = 5 cm.
Hence, half of PQ is = = .
Then the segment PQ itself is = 26.1534 cm (rounded) ANSWER
Solution 2
You can apply the intersecting chords theorem - but you should to use it in correct way.
Then two parts of the horizontal chord are x cm each,
while two parts of the vertical chord are 9 cm and 5+14 = 19 cm.
The intersecting chords theorem takes the form
x*x = 9*19, or x^2 = 171, x = , PQ = 2x = = 26.1534 cm (rounded) ANSWER
giving the same number.
Solved.
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On the intersecting chords theorem, see the lesson
- The parts of chords that intersect inside a circle,
in this site.