Calculus
posted by Mark .
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?

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(489) (1)
R = 39