Related Rates Problem (Check work)

In summary, as the square expands, the circle expands to maintain the four points of intersection. The perimeter of the square is expanding at a rate of 8 inches per second, which results in the diagonal of the square increasing at a rate of 2√2 inches per second. This in turn causes the circumference of the circle to increase at a rate of 2√2π inches per second.
  • #1
sportsguy3675
45
0
A square is inscribed in a circle. As the square expands, the circle expands to maintain the four points of intersection. The perimeter of the square is expanding at the rate of 8 inches per second.

Find the rate at which the circumference of the circle is increasing.

Perimeter = p
diameter/diagonal = d
circumference = C

p = 2d sqrt2
p = 2sqrt2 d
dp/dt = 2sqrt2 dd/dt
dd/dt = 8 / 2sqrt2
dd/dt = 2sqrt2 in/sec

C = pi d
dC/dt = pi dd/dt
dC/dt = 2sqrt2 pi in/sec

Is that correct for the rate of the circumference?
 
Last edited:
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  • #2
Yes. I might recommend using some letter other than "d" to represent the length of the diagonal (so you don't get that "dd/dt" stuff) but you work is correct.
 
  • #3
OK. Thanks :)
 

1. How do I determine which variables are related in a related rates problem?

In a related rates problem, the variables that are related are typically the ones that are changing with respect to time. This can be determined by carefully reading the problem and identifying which quantities are dependent on each other.

2. Are there any specific steps or strategies for solving related rates problems?

Yes, there are some general steps and strategies that can be used to solve related rates problems. These include identifying the variables, writing an equation that relates the variables, differentiating the equation with respect to time, plugging in known values, and solving for the desired rate.

3. How can I check if my solution to a related rates problem is correct?

One way to check the solution is to plug in the values given in the problem and see if the resulting rates match what was given. Another way is to graph the equations and see if the rates at a specific point match the given rates.

4. Can I use any differentiation rules when solving related rates problems?

Yes, you can use any differentiation rule that is applicable to the equation being used in the problem. This can include the power rule, product rule, quotient rule, and chain rule.

5. Are there any common mistakes to avoid when solving related rates problems?

One common mistake is to mix up the variables and their rates, especially when there are multiple variables involved. It is important to carefully label and keep track of which variables are changing with respect to time. Another mistake is not using the correct units for the rates, which can result in an incorrect solution.

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