Title: Related Rates PostVideo Questions
Course: Calculus I

Q: A circle's radius, r, is increasing at a rate of 3 inches per second, as shown below. How quickly is its area increasing? (The formula for the area of a circle is A = π(r)^(2).)
[Image: image]
- 5 π r square inches per second (Incorrect)
- 3 π r square inches per second (Incorrect)
- 6 π r square inches per second (Correct)
- 2 π r square inches per second (Incorrect)
- There is not enough information to answer this question (Incorrect)
A: 6 π r square inches per second

Q: A submarine is diving at a rate of 50 feet per minute. As the sub descends, the water temperature outside is falling at a rate of 0.5 degrees per foot. let D be the depth of the submarine. Let T be the temperature outside the submarine. How quickly is the temperature falling?
- 25 degrees per minute (Correct)
- 50 degrees per minute (Incorrect)
- 0.5 degrees per foot (Incorrect)
- 100 degrees per minute (Incorrect)
- There is not enough information to answer this question (Incorrect)
A: 25 degrees per minute

Q: A rectangle has a constant height of 6 cm while the base's length is decreasing at a constant rate of 3 cm/sec, as shown below. The area of the rectangle is given by the formula A = b h, where b is the length of the base of the rectangle and h is the height of the rectangle. In order to determine how fast its area is changing at the instant that the base has length 8 cm, which of the following formulas would you use?
[Image: image]
- (d A)/(d t)=(d A)/(d b)·(d b)/(d t) (Correct)
- (d A)/(d h)= b (Incorrect)
- (d A)/(d t)=(d A)/(d h)·(d h)/(d t) (Incorrect)
- (d A)/(d b)= h (Incorrect)
A: (d A)/(d t)=(d A)/(d b)·(d b)/(d t)