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Korvikt [17]
3 years ago
8

A circle has an initial radius of 50ft when the radius begins decreasing at a rate of 2ft/s. what is the rate of change of the a

rea at the instant the radius is 10ft?
Physics
1 answer:
valkas [14]3 years ago
7 0
The area of the circle with radius r is
A = πr²

The rate of change of area with respect to time is
\frac{dA}{dt} = \frac{dA}{dr} . \frac{dr}{dt} =2 \pi r. \frac{dr}{dt}

The rate of change of the radius is given as
\frac{dr}{dt} =-2 \,  \frac{ft}{s}
Therefore
\frac{dA}{dt} =-4 \pi r \,  \frac{ft^{2}}{s}

When r = 10 ft, obtain
\frac{dA}{dt}|_{r=10 \, ft} = -40 \pi  \,  \frac{ft^{2}}{s}

Answer: - 40π ft²/s (or - 127.5 ft²/s)
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