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19 June, 21:46

Cells in the body of a metazoan organism like yourself have many shapes and sizes that are suited to their particular functions. Consider a muscle cell, which has the shape of a long cylinder. A cell in one of the tiny dorsal interosseous muscles of your hand is 13 mm long, with a radius of 10 μm. (A) What is its surface-to-volume ratio?

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  1. 19 June, 22:15
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    Given:

    Muscle cell have cylindrical shape.

    Height of the cylinder = 13mm

    Radius of the cylinder = 10μm

    Surface to volume ratio = ?

    Solution -

    Converting the units to meter (m):

    Height:

    1mm = 0.001m

    13mm = 0.013m

    Radius:

    1 μm = 10-6 m

    10 μm = 10-5 m

    Surface area of cylinder=2πr^2+2πrh

    Surface area of cylinder=2πr (r+h)

    Volume of cylinder=πr^2 h

    Surface to volume ratio = (2πr (r+h)) / (πr^2h)

    Surface to volume ratio = (2 (r+h)) / rh

    Putting the values in the above equation gives;

    Surface to volume ratio = (2 (0.00001+0.013)) / (0.00001*0.013)

    Solving the equation gives,

    Surface to volume ratio=200154 m^-1
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