# Calculus

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A spherical fish tank of radius 8 meters is being filled with at a constant rate of Rπ meters cube of water per second. At height 3 meters, the rate of change of the height is 1 meter per second. What is the value of R?

• Calculus -

When the water is of height y, the volume is

v = pi/3 y^2 (3*8 -y) = 8pi y^2 - pi/3 y^3
dv/dt = pi(16y - y^2) dy/dt
When y=3,
R pi = pi(48-9) (1)
R = 39

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