You are here:

- Home
- Science
- Mathematics
- Advanced Math
- Math Word Problem

Advertisement

A farmer has 100 m of mobile fence to build an enclosure. He hesitates between a square enclosure and a circular enclosure. What shape of enclosure should he build to enclose the maximum area?

The 100 m length corresponds to the perimeter of the enclosure, P.

P_circle = 2πr = 100 ⇒ r = 100/(2π)

P_square = 4･r = 100 ⇒ r = 25

Areas:

A_circle = πr^2 = 10000/(4π) = 796 m^2

A_square = r^2 = (25)^2 = 625 m^2

So the circle has a larger area for the same perimeter.

- Add to this Answer
- Ask a Question

Rating(1-10) | Knowledgeability = 10 | Clarity of Response = 8 | Politeness = 10 |

Comment | No Comment |

Advanced Math

Answers by Expert:

college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related **Publications**

J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane**Education/Credentials**

M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math**Past/Present Clients**

Also an Expert in Oceanography