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?

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