Question

When oil was spilled out in the middle of a lake, it spread out on the surface of the water in a circular pattern. The radius of the circular pattern increased at a rate of 4 feet per minute.((() = 4tft/min)Find the radius and area of the circular pattern of oil 5 minutes after the oil starts to spread.

Answer 1

The radius of the circle increases by 4 feet per minute. When 1 minute has passed, the radius is 4 feet, and when 5 minutes have passed, the radius will be 5 times that:

`4*5=20`

The radius of the circle after 5 minutes is 20 feet.

To find the area, we use the formula for the area of a circle:

`A=\pi r^2`

Using the radius of 20 feet:

`r=20ft`

And substituting it into the formula for the area:

`\begin{gathered} A=\pi(20ft)^2 \\ A=\pi(400ft^2) \end{gathered}`

Using:

`\pi=3.1416`

We get the are of the circular pattern:

`\begin{gathered} A=(3.1416)(400ft^2) \\ A=1,256.64ft^2 \end{gathered}`

Answer:

`\begin{gathered} r=20ft \\ A=1,256.64ft^2 \end{gathered}`