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A circle is inside a square. The radius of the circle is decreasing at a rate of 4 meters per minute and the sides of the square are decreasing at a rate of 1 meter per minute. When the radius is 2 meters, and the sides are 24 meters, then how fast is the AREA outside the circle but inside the square changing

Respuesta :

razorsharptip

Answer: (16pi-48) m^2/min  

Step-by-step explanation:

If the area of the circle is pi * r^2, and the area of the square is s^2, then the area outside the circle but inside the square is:

A = s^2 - pi * r^2

differentiate both sides

dA/dt = 2s * ds/dt - 2pi * r * dr/dt

dA/dt = 2 * 24 * -1 - 2pi * 2 * -4

dA/dt = 16pi - 48 m^2/min