Related Rates

Front

What is the formula for the volume of a sphere?

Back

Front

Define related rates in calculus.

Back

Related rates are used to find the rate at which one quantity changes with respect to another quantity that is also changing.

Front

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

Back

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

Front

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

Back

The volume of a sphere increases with the cube of the radius, meaning if the radius increases, the volume increases at a faster rate.

Front

If the volume of a balloon is increasing at a rate of 8 in³/sec, how do you express this in terms of the radius?

Back

Front

What is the derivative of the volume of a sphere with respect to time?

Back

Front

How do you find the rate at which the area of a circle is changing?

Back

Front

What is the formula for the area of a circle?

Back

Front

In the ladder problem, what is the relationship between the height of the ladder and the distance from the wall?

Back

Front

What does a negative rate of change indicate in related rates problems?

Back

A negative rate of change indicates that the quantity is decreasing over time.