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Math / Numerical Analysis 9 / Chapter 2.1 / Problem 19

Numerical Analysis | 9th Edition | ISBN: 9780538733519 | Authors: Richard L. Burden, J. Douglas Faires

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A trough of length L has a cross section in the shape of a semicircle with radius r

Chapter 2, Problem 19

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QUESTION:

A trough of length L has a cross section in the shape of a semicircle with radius r. (See the accompanying figure.) When filled with water to within a distance h of the top, the volume V of water is V = L 0.5r2 r2 arcsin(h/r) h(r2 h2 ) 1/2 . h h r Suppose L = 10 ft,r = 1 ft, and V = 12.4 ft3. Find the depth of water in the trough to within 0.01 ft.

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QUESTION:

A trough of length L has a cross section in the shape of a semicircle with radius r. (See the accompanying figure.) When filled with water to within a distance h of the top, the volume V of water is V = L 0.5r2 r2 arcsin(h/r) h(r2 h2 ) 1/2 . h h r Suppose L = 10 ft,r = 1 ft, and V = 12.4 ft3. Find the depth of water in the trough to within 0.01 ft.

ANSWER:

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