If the radius r of a circle is decreasing at the rate of 5 cm per minute, find the rate of change of area when radius is 6 cm.

The area decreases at a rate of -188.4 square centimeter per minute

The area (A) of a circle of radius (r) is represented as:

Differentiate the area, with respect to r

From the question, we have:

So, the equation becomes

Hence, the area decreases at a rate of -188.4 square centimeter per minute

Read more about rates of change at:

link

-94.2

Step-by-step explanation:

Rate of change of radius = -5 cm per minute (as it is decreasing)

Radius of circle = 6 cm

Formula for area of Area:

Formula for differentiation of :

Differentiating area w.r.to :

Putting the values, cm per minute.

Negative sign indicates that area is decreasing.

Rate of change of area is -94.2 .

boxplot

they used 313 gallons of paint