Differentiation of Geomertic Objects

[thomas49th]

[URGENT] Differentiation of Geomertic Objects

Homework Statement

A sector of a circle has area 100cm². Show that the perimeter of this sector is given by te formula P = 2r + 200/r

Homework Equations

Area of sector = (angle/360) x pi x r^2
Permiter of sector = (angle/360) x 2 pi x r

The Attempt at a Solution

I've tried but i don't really have time to write it all out. Can someone just show me how to do this one, so that i can try the other questions in the chapter

Thanks

 

[jhicks]

There's no differentiation involved that I see. Your "perimeter equation" is actually the equation of the arc length of a circle of radius r through angle theta. The actual equation would be the sum of the arclength as well as the two segments which go from the radius inward toward the center of the circle.

Your area equation has 2 different parameters, r and theta. Given an r, you can find theta, so solve for theta in that equation and plug it into your equation for the perimeter. Use theta in radians.