Water is slowly leaking from a bird bath at the rate of 8 cm3/min. The birdbath is in the shape of a cone with the vertex down and the radius is double the height. How fast is the water level changing when the water is 10 cm deep

The water level is changing at - 0.016 centimeters per minute when the water is 10 centimeters deep.

Step-by-step explanation:

From Geometry, the volume of the cone (), measured in cubic centimeters, is defined by:

(1)

Where:

- Radius, measured in centimeters.

- Height, measured in centimeters.

Then, we find a formula for the rate of change of the volume of the birth bath (), measured in cubic centimeters per minute, by means of differentiation:

(2)

Where:

- Rate of change of radius, measured in centimeters per minute.

- Rate of change of height, measured in centimeters per minute.

In addition, we have the following relationship:

(3)

And by Differential Calculus:

(4)

By applying (3) and (4) in (2), we find the following expanded formula:

(5)

If and , then the rate of change of the water level is:

The water level is changing at - 0.016 centimeters per minute when the water is 10 centimeters deep.

$9.89

step-by-step explanation:

9.90 = p x .06 x .25 (3/12 changed to a decimal)

9.90 = p x 0.015

9.90 - 0.015 = p

9.89 = p