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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 Ī¼m. (A) What is its surface-to-volume ratio?

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Respuesta :

Given :

Muscle cell have cylindrical shape.

Height of the cylinder = 13mm

Radius of the cylinder = 10Ī¼m

Surface to volume ratio = ?

Solution ā€“

Converting the units to meter (m):

Height:

1mm = 0.001m

13mm = 0.013m

Radius:

1 Ī¼m = 10-6 m

10 Ī¼m = 10-5 m

Ā Surface area of cylinder=2Ļ€r^2+2Ļ€rh

Ā Surface area of cylinder=2Ļ€r (r+h)

Volume of cylinder=Ļ€r^2 h

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

Surface to volume ratio= Ā (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 Ā 

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