Asked by Marney
If a hemispherical bowl of radius 6cm contains water to a depth of h cm, the volume of the water is 1/3πh^2(18-h). Water is poured into the bowl at a rate 4 cm^3/s . Find the rate at ehich the water level is rising when the depth is 2 cm.
Answers
Answered by
Reiny
V = (1/3)πh^2 (18-h)
= 6πh^2 - (1/3)πh^3
dV/dt = 12πh dh/dt - πh^2 dh/dt
4 = dh/dt(12πh - πh^2)
when h = 2
4 = dh/dt(24π - 4π)
dh/dt = 4/(20π) = 1/(5π) cm/s
= 6πh^2 - (1/3)πh^3
dV/dt = 12πh dh/dt - πh^2 dh/dt
4 = dh/dt(12πh - πh^2)
when h = 2
4 = dh/dt(24π - 4π)
dh/dt = 4/(20π) = 1/(5π) cm/s
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.