Share
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 radiu
Question
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
in progress
0
Mathematics
3 years
2021-07-20T14:55:26+00:00
2021-07-20T14:55:26+00:00 1 Answers
12 views
0
Answers ( )
Answer:
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.