Saturday

January 31, 2015

January 31, 2015

Posted by **sunny** on Wednesday, May 8, 2013 at 1:03am.

circles at the ends with a possible rectangular area between the semi-circles, determine

the dimensions of the rectangle and semi-circles that will maximize the total area.

- math -
**Reiny**, Wednesday, May 8, 2013 at 6:54amLet the radius of the end sem-circles be r

making the width of the rectangle to be 2r

let the length of the rectangle be x

The perimeter of the field is 2x + 2πr

= 1400

x + πr = 700

x = 700-πr

area = πr^2 + 2rx

= πr^2 + 2r(700-πr)

= πr^2 + 1400r - 2πr^2

d(area)/dr = 2πr + 1400 - 4πr = 0 for a max of area

1400 - 2πr = 0

2πr = 1400

r = 700/π

then x = 700 - π(700/π) = 0

Unexpected strange result!

BUT there is nothing wrong with the calculations, it is the wording of the question that is flawed.

Of course the largest area of any region with a given perimeter is a circle, which my solution has shown.

**Answer this Question**

**Related Questions**

Geometry - I have a picture of a window showing a square in the center with ...

calc - Given that a window entails a rectangle capped by a semi-circle, given ...

maths - This taxi sign is 2.1 metres wide and 39cm tall. Assuming the ends are ...

Maths - the figure below shows 3 similar circles that just touch one another.A,...

Math (Circles) - True or False If two circles have 4 common tangents, then the ...

Math - Garden Area Problem. A designer created a garden from two concentric ...

geometry - how can you determine the probability that a point radomly selected ...

Math...again - Two circles have circumferences of π and 3π. What is ...

Math...anyone? - Two circles have circumferences of π and 3π. What is ...

GEOMETRY(CIRCLE) - Three circles with different radii have their centers on a ...