Mathematics, 21.01.2021 22:10 59bobolucci
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
Answers: 3
), measured in cubic centimeters, is defined by:
(1)
- Radius, measured in centimeters.
- Height, measured in centimeters. 
), measured in cubic centimeters per minute, by means of differentiation:
(2)
- Rate of change of radius, measured in centimeters per minute. 
- Rate of change of height, measured in centimeters per minute. 
(3)
(4)![\dot V = \frac{\pi}{3}\cdot \left[2\cdot (2\cdot h)\cdot (2\cdot \dot h)+4\cdot h^{2}\cdot \dot h\right]](/tpl/images/1053/5494/b2e4c.png)
(5) 
and 
, then the rate of change of the water level is:
![\dot h = \frac{-8\,\frac{cm^{3}}{min} }{\frac{\pi}{3}\cdot [8\cdot (10\,cm)+4\cdot (10\,cm)^{2}] }](/tpl/images/1053/5494/01023.png)
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Water is slowly leaking from a bird bath at the rate of 8 cm3/min. The birdbath is in the shape of a...
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