# Re: pre-cal question

[ Follow Ups ] [ Post Followup ] [ Calculus Message Board ] [ FAQ ]

Posted by T.Gracken on September 18, 2002 at 13:38:38:

In Reply to: pre-cal question posted by Brandi on September 16, 2002 at 15:04:52:

: I have a question. There is a semi-circle with a rectangle in it. The radius of the semi-circle is 10. I am supposed to find a function that models the area A of the rectangle in terms of its height h. The answer is A(h) = 2h(square root 100-h squared) when 0: Can you help?!

: Brandi
: sorry for sending so many times.

without a picture, this may be difficult to follow, but here's my attempt (not the fake T.G. who put the nonsensical "but......." reply)

I assume the rectangle has vertices (corners) touching the semi-circle. I will also assume the semi-circle is drawn with its base horizontal (top half of a circle) for visual referrence.

let h = the height of the rectangle

let x = the distance from the center of the semi-circle base to the right edge of the rectangle (along the base)

then the area of the rectangle is A = 2xh ...which is the same as A = 2hx

Now... notice that if you draw a line from the center of the base to the top right corner of the rectangle, you can label the sides of the (right) triangle created as follows: x for the base, h for the height, and 10 for the hypotenuse.

from the Pythagorean theorem, you get: x2 + h2 = 102

or x2 + h2 = 100

giving x2 = 100 - h2

leading to x = sqrt(100 - h2) ...[note no + or - since x must be between 0 and 10 exclusive or no rectangle is formed]

so substitute into the above formula and wallah!

A = 2h[sqrt(100 - h2)]

is that what you werre looking for???

Name:
E-Mail:

Subject: