A cylindrical tank standing upright has radius 20cm. If the water is being drained at rate 25 cm³/s the tank level drops at rate 0.02 cm/s.
Recall the formula for the volume of a cylinder:
V = πr². h
Where:
r = radius of the base
h = height of the cylinder
Take the derivative with respect to t
dV/dt = πr². dh/dt
Substitute dV/dt = 25 cm³/s and r = 20 cm:
25 = π x 20² x dh/dt
dh/dt = 25 / (400π) = 0.02 cm/s
Therefore, the level of the cylindrical tank drops at rate 0.02 cm/s
Complete question:
A cylindrical tank standing upright has radius 20cm. How fast does the water level in the tank drop when the water is being drained at 25 cm³/s?
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