Posted by **Ashley** on Tuesday, January 29, 2013 at 8:45am.

A mechanical engineering student wishes to inscribe a rectangle in a quarter circle of radius 2.00 cm. Determine the dimensions of the rectangle that will give it the greatest area.

length in cm =

height in cm =

My attempt on find the relationship between the rectangle and the quarter circle:

Let the base of the rectangle = b

let the height of the rectangle = h

Area of a a rectangle = b*h

Area of a circle =pie*R^2

Quarter of a circle = 1/4 pie R^2

am I on the right track......

is this the correct thought process....

- Math -
**Ashley**, Tuesday, January 29, 2013 at 8:52am
Would it be safe to say that the the diagonal line in the rectangle could equal r = 2.

so I could use

b^2+ h^2 =r^2

solve for h

h= Square root ( r^2 -b^2)

Area = b^2 * Square root (r^2-b^2)

area = b*(r^2-b^2)^1/2 ....... ????

- Math -
**Norman**, Tuesday, January 29, 2013 at 10:04am
Ok

- Math -
**Ashley**, Tuesday, January 29, 2013 at 10:44am
ok....

so is next step take the first derv of the area

Area of rect '= -1/2(4-b^2) + (4-2^2)^1/2

## Answer This Question

## Related Questions

- math - A Norman window has the shape of a rectangle surmounted by a semicircle...
- Math - If the length of a rectangle is (2x-1)cm and its width is (x+3)cm. How do...
- math - a rectangle is twice as long as it is wide. if both of its dimensions are...
- Math - A rectangle is inscribed in a semi circle of radius 2, let x represent ...
- Math - A rectangle is inscribed in a circle of radius r. If the rectangle has ...
- calculus - A rectangle is to be inscribed in a right triangle having sides of ...
- Math - You have 300 meters of fencing with which to build two enclosures. One ...
- Math - A rectangle is inscribed with its base on the x-axis and its upper ...
- Math - A rectangle has a length of 6 cm in an area of 24 cmÂ². If the radius of ...
- Math - The area of a rectangle is shown below The area of the rectangle is 56 ...

More Related Questions