4. A sport fishing club is putting on a fishing derby near Hypothetical, TX. Onl

Question

4. A sport fishing club is putting on a fishing derby near Hypothetical, TX. Only bass qualify towards trophies, and only the weight of the fish matters. However, since easily portable scales are notoriously inaccurate when weighing live fish, the club sponsors want a different way to weigh the fish. You should come up with a formula that should be easy to understand and compute quickly on a 4-function calcula- tor. However, rather than force people to use a calculator, you should make an easy to use (small) card that compares length versus girth to give weight (but has the formula listed for values not covered)

Explanation / Answer

assuming the fist to be a cylinder

we get volume = pi * r^2 * l

l is length of fish and r is radius

now volume = c^2 *l / 12.5

now to get weight we have v*d

d is the average density of the fish

so we have weight - c^2 *l *d / 12.5 = c^2*l*K

where k is the constant

we can get d as the average density of all fish caught in the past

typical formulas used in competitions are

c^2*l/927

in pounds

but it's best to estimate the constant k using real data.

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