What does it mean when the area of a puddle decreases at a rate of $$36\pi \frac{in^2}{hr}$$ ?

It means that the area is shrinking, and this rate can be expressed as $$\frac{dA}{dt} = -36\pi \frac{in^2}{hr}$$ .

How do you calculate the rate of change of the radius when the area is decreasing?

You can rearrange the area formula to find $$\frac{dr}{dt} = \frac{\frac{dA}{dt}}{2\pi r}$$ .

What is the rate of change of the volume of a snowball when its radius is 2 in and increasing at 2 in/sec?

$$\frac{dV}{dt} = 32\pi \frac{in^3}{sec}$$ .

What is the relationship between the radius and volume of a sphere in terms of calculus?

The rate of change of volume with respect to time is given by $$\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}$$ .

How do you express the rate of change of area in terms of radius?

$$\frac{dA}{dt} = 2\pi r \frac{dr}{dt}$$ .

What does $$\frac{dr}{dt} = -3.6 \frac{in}{hr}$$ indicate about the radius of the puddle?

It indicates that the radius is decreasing at a rate of 3.6 inches per hour.

How do you determine the rate of change of the radius when given the rate of change of the area?

Use the relationship $$\frac{dr}{dt} = \frac{\frac{dA}{dt}}{2\pi r}$$ to find the rate.

CalcAB Related Rates

Flashcard

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Mathematics

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12th Grade

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Practice Problem

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Hard

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CCSS

7.G.B.4, 8.G.C.9, 8.EE.A.2

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