Consider a water tank filling at a rate of A cubic metres per minute. The structure of tank has a cube of side L at its base, and a cylinder kept on the cube such that the flat circular part of cylinder touches the four edges of one face of the cube. The height of cylinder is h. What is the rate of change of height from the ground if the water surface is in cylinder now?
Answers
Given : a water tank filling at a rate of Q cubic metres per minute
The structure of tank has a cube of side L at its base, and a cylinder kept on the cube such that the flat circular part of cylinder touches the four edges of one face of the cube.
The height of cylinder is h.
To Find : What is the rate of change of height from the ground
Solution:
a cylinder kept on the cube such that the flat circular part of cylinder touches the four edges of one face of the cube.
Hence Diameter of cylinder = L
=> Radius = L/2
height of cylinder is h.
Volume of cylinder V = π (L/2)² h = πL²h/4
V = πL²h/4
dV/dt = ( πL²/4) dh/dt
dV/dt = Q m³ / min
( πL²/4) dh/dt = Q
=> dh/dt = 4Q/ πL²
rate of change of height from the ground = dh/dt = 4Q/ πL²
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