What is the relationship between area and radius?

The area of a circle is given by the formula $$A=\pi r^2$$ .

How do you find the rate of change of area with respect to time?

Use the chain rule: $$\frac{dA}{dt}=\frac{dA}{dr}\cdot\frac{dr}{dt}$$ .

If the radius is increasing at a rate of 5 ft/sec, how fast is the area increasing when the radius is 10 ft?

$$\frac{dA}{dt}=2\pi(10)(5)=100\pi\ ft^2/sec$$ .

If the circumference is increasing at a rate of 40 ft/sec, what is the relationship to the radius?

$$\frac{dC}{dt}=2\pi\cdot\frac{dr}{dt}$$ implies $$\frac{dr}{dt}=\frac{20}{\pi}$$ .

What is the significance of related rates in real-world applications?

Related rates help in solving problems involving changing quantities, such as speed, volume, and area in various fields like physics and engineering.

How do you set up a related rates problem?

Identify the quantities involved, write down the relationships between them, and differentiate with respect to time.

Intro to Related rates Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the rate of change of circumference with respect to time when the circumference is increasing at 40 ft/sec?

Back

2.

FLASHCARD QUESTION

Front

What is the rate we are looking for when the circumference of the circle is 100π ft?

Back

3.

FLASHCARD QUESTION

Front

What is the formula for the derivative of circumference with respect to time?

Back

4.

FLASHCARD QUESTION

Front

What is the formula for the derivative of area with respect to time?

Back

5.

FLASHCARD QUESTION

Front

How is the radius changing when the circumference is 100π ft?

Back

6.

FLASHCARD QUESTION

Front

Define related rates in calculus.

Back

Related rates are used to find the rate at which one quantity changes with respect to another quantity that is also changing.

7.

FLASHCARD QUESTION

Front

What is the relationship between circumference and radius?

Back

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