A forest fire spreads outward from a central point in a circular path. The dista

Question

A forest fire spreads outward from a central point in a circular path. The distance from the center of the fire to the outer edge of the fire is increasing at a rate of 8 feet per hour. Express the area encompassed by the fire, A in terms of time t in hours. A forest fire spreads outward from a central point in a circular path. The distance from the center of the fire to the outer edge of the fire is increasing at a rate of 8 feet per hour. Express the area encompassed by the fire, A in terms of time t in hours.

Explanation / Answer

Given that fore spreads from central point in a circular path.

The rate of increase in distance is 8ft/hr.

Hence for t hrs the radius from center is 8t ft.

The area encompassed by fire is circle with radius 8t.

Hence area = pi * r^2

=3.14 * r^2 = 3.14*(8t)^2

=200.96t^2 sqft

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