creating a circular ripple that travels outward at a speed of 60 cm/sec. Express the area of this circle as a function of time (in seconds).

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## Answers (1)

The area of any circle is πr², where r is the radius of the circle.

But what is the radius of the circle as a function of time. The ripple travels outward at a speed of 60 cm/sec, or 0.6 m/s. That means the radius is increasing by 0.6 m every second, and if t is the number of seconds passed, then the radius of the circle is r = 0.6t.

And the area of the circle in metres will be given by π(0.6t)² = 0.36πt²