Related Rates Unit 4

Front

What is the formula for the volume of a sphere?

Back

Front

What does it mean for the volume of a sphere to decrease at a constant rate?

Back

It means that the volume is reducing by the same amount every second, which can be expressed as a negative rate of change.

Front

How do you find the rate of change of the radius of a sphere when the volume is changing?

Back

Use the relationship between volume and radius, and apply the chain rule to differentiate with respect to time.

Front

What is the formula for the volume of a cone?

Back

Front

How do you find the rate at which water is being poured into a conical cup?

Back

Differentiate the volume formula with respect to time and substitute the known rates of change.

Front

What is related rates in calculus?

Back

Related rates involve finding the rate at which one quantity changes in relation to another quantity that is also changing.

Front

What is the relationship between the height and radius of a cone when water is being poured in?

Back

The height and radius of the cone are related through the geometry of the cone, often requiring the use of similar triangles.

Front

How do you determine the rate of change of an angle in a right triangle?

Back

Use trigonometric relationships and implicit differentiation to find the rate of change of the angle with respect to time.

Front

What is the significance of the negative sign in rates of change?

Back

A negative sign indicates that the quantity is decreasing over time.

Front

How do you calculate the rate of change of the radius of a balloon when its volume is increasing?

Back

Use the volume formula for a sphere and differentiate with respect to time, then solve for the rate of change of the radius.