SOLUTION: HI PLEASE I NEED YOUR HELP WITH THE QUESTION BELOW The cochlea is a coiled cylindrical tube that forms the auditory portion of the ear. A cochlear tube with a radius of 4.05 mm

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Question 1154286: HI
PLEASE I NEED YOUR HELP WITH THE QUESTION BELOW
The cochlea is a coiled cylindrical tube that forms the auditory portion of the ear. A cochlear tube with a radius of 4.05 mm occupies 1.40 cm3, what is the length of the coiled tube inside the ear? Round your answer to 3 significant digits.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The cochlea is a coiled cylindrical tube, so you need formula of volume of cylinder:
V=+pi%2Ar%5E2%2Ah+where r is a radius and h is height (in your case length )

if a cochlear tube has a radius of r=4.05mm and occupies V=1.40cm%5E3,

1.40cm%5E3=+pi%284.05mm%29%5E2%2Ah+......convert cm%5E3+to mm%5E3: 1cm%5E3=1000mm%5E3=>1.40cm^3= 1.40*1000mm^3=1400mm^3

h=1400mm%5E3%2F%28pi%2816.4025mm%5E2%29%29
h=1400mm%2F%28pi%2816.4025%29%29
h=1400mm%2F51.52997350050658
h=27.169mm=>the length of the coiled tube inside the ear