A straw is used to drink soda from the bottom of a cylindrical shaped cup. The diameter of the cup is 3 inches.
Qn(a) The liquid is being consumed at a rate of 1 cubic inches per seconds.
How fast is the level of the soda dropping in inches/sec? (Accurate to 2dp)
Qn(b)The liquid is being consumed at a rate of 2 cubic inches per seconds.
How fast is the level of the soda dropping in inches/sec? (Accurate to 2dp)
A straw is used to drink soda from the bottom of a cylindrical shaped cup. The diameter of the cup is 3 inches.?
2016-03-27 5:35 am
回答 (1)
2016-03-27 6:27 am
Volume for soda in cylindrical cup = base area of cup x height of soda
V = π(d²/4)h
V = π(3²/4)h
V = (9π/4)h
To find rate find derivative with respect to time
dV/dt = ((9π/4)dh/dt
dh/dt = (4/9π)dV/dt
When dV/dt = 1 cu in /sec
dh/dt = (4/9π) 1 = 0.14 in / sec drop in level
When dV/dt = 2 cu in /sec
dh/dt = (4/9π) 2 = 0.28 in / sec drop in level
V = π(d²/4)h
V = π(3²/4)h
V = (9π/4)h
To find rate find derivative with respect to time
dV/dt = ((9π/4)dh/dt
dh/dt = (4/9π)dV/dt
When dV/dt = 1 cu in /sec
dh/dt = (4/9π) 1 = 0.14 in / sec drop in level
When dV/dt = 2 cu in /sec
dh/dt = (4/9π) 2 = 0.28 in / sec drop in level
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