A square is inscribed in a circle. As the square expands, the circle expands to maintain the four points of intersection. The perimeter of the square is expanding at the rate of 8 inches per second. Find the rate at which the circumference of the circle is increasing. Perimeter = p diameter/diagonal = d circumference = C p = 2d sqrt2 p = 2sqrt2 d dp/dt = 2sqrt2 dd/dt dd/dt = 8 / 2sqrt2 dd/dt = 2sqrt2 in/sec C = pi d dC/dt = pi dd/dt dC/dt = 2sqrt2 pi in/sec Is that correct for the rate of the circumference?