How to solve a changing area of circle with related rates

The video tutorial explains a problem involving ripples forming in circles, where the radius of the outer ripple increases at a rate of 1 foot per second. The teacher emphasizes understanding the question to avoid solving for the wrong material. Given that the radius is 4 feet, the tutorial guides through differentiating the area formula with respect to time to find the rate of change of the disturbed area. The solution involves calculating the derivative of the area with respect to time, resulting in a rate of 8π square feet per second.

What is the rate at which the radius of the outer ripple increases?

• 2 feet per second

• 1 foot per second

• 3 feet per second

• 4 feet per second

Why is it important to restate the question in word problems?

• To change the problem entirely

• To make the problem more complex

• To confuse the students

• To ensure the correct question is being answered

When the radius is 4 feet, what are we trying to find?

• The rate of change of the radius

• The total area of the disk

• The rate of change of the area

• The circumference of the ripple

What is the formula used to find the rate of change of the area with respect to time?

• DA/DT = πR^2

• DA/DT = 2πR * DR/DT

• DA/DT = R^2 * DR/DT

• DA/DT = 2πR

What is the value of DA/DT when the radius is 4 feet and DR/DT is 1 foot per second?

• 4π feet squared per second

• 8π feet squared per second

• 10π feet squared per second

• 6π feet squared per second