sorry Mr. S, I didn't realize you already posted a similar response to what I wrote above -nt-

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: : : 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<h<10. : : : Can you help?! : : : Brandi : : First of all, Brandi, asking four times won't get you the answer faster. : : Many many questions to ask. : : Did you drew a sketch? : : Do you know the equation of a circle? (No, not the area.) : : Do you know the formula for the area of a rectangle? : : I'll try to explain this without a diagram - tricky! : : You have your semicircle centered at the origin, extending left to right : : from -10 to 10. It extends upward from 0 to 10. : : About halfway up the semicircle, draw a horizontal line. : : It cuts the Y-axis at h. That's the height of the rectangle. : : Where the line cuts the semicircle (left and right) is the length. : : Draw lines straight down to the X-axis. There is : : our rectangle! : : Since the area of a rectangle is Length x Width : : (or Length x Height), : : we need to find the Length. : : The equation of that circle is: x^2 + y^2 = 100. : : For y = h, we solve x^2 + h^2 = 100, and get x = sqrt(100 - h^2) : : But that's the distance from 0 to the right side of the rectangle. : : The Length is twice that. So, Length = 2sqrt(100-h^2) : : We've got it! : : Area = Length x Height = 2h sqrt(100-h^2)

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