Question
The radius of a circular oil slick expands at a rate of
.
(a) How fast is the area of the oil slick increasing when the radius is 22 m ?
(b) If the radius is 0 at time
, how fast is the area increasing after 3 mins ?
(a) How fast is the area of the oil slick increasing when the radius is 22 m ?
(b) If the radius is 0 at time
Ask by Ingram Powers. in the United States
Mar 15,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
(a) When the radius is 22 meters, the area is increasing at
.
(b) After 3 minutes, the area is increasing at
.
Solution

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Bonus Knowledge
To determine how fast the area of the oil slick is increasing, we need the formula for the area of a circle, which is
. By using related rates, we can find
.
(a) The formula for the area is
. To find the rate of change of area with respect to time, we differentiate both sides with respect to
:
Substituting
and
:
Calculating
, so:
(b) After 3 minutes, the radius will increase by
. Therefore, the radius at this time is:
Again, using the area expansion formula:
Calculating
, so: