Homework SourseThe volume of paint in a right cylindrical can is given by V
The volume of paint in a right cylindrical can is given by V = 2t2 ? t where t is time in seconds and V is the volume in cm3. How fast is the level rising when the height is 2 cm? The can has a height of 4 cm and a radius of 1 cm. HINT [To get h as a function of t, first solve the volume
V = ?r2h for h.]
(Give the answer to one decimal place.) Maybe it\'s late and I\'m tired, but I\'m confused.
V = ?r2h for h.]
(Give the answer to one decimal place.) Maybe it\'s late and I\'m tired, but I\'m confused.
Solution
V = 2t2 + t
Also, V = r2h
t(2t+1) = r2h
For cylinder, r = fixed = 1cm
h = (1/)(2t2 + t)
h = 2cm
2 = 2t2+t => t = 77/50
h = (1/)V
dh/dt = (1/)dV/dt
dh/dt = (1/)(4t+1) = (1/)(4x77/50 + 1) = 2.28 cm/sec
