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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?

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?

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