Question

A certain spherical eukaryotic cell has a diameter of 51um. If a spherical organelle has a diameter of 860nm, how many of these organelles can the cell hold.

Answer 1

To find the number of oraganelles the eukaryotic cell can hold first we have to determine the volume of organelles and the eukaryotic cell.

As the cell and the organelles are of spherical shape,

Volume of sphere = (4/3)*π* r³                         (π = 22/7)

Radius of eukaryotic cell = Diameter / 2 = (51) / 2 um = 2.55 * 10^-5 m      (1 um = 10^-6 m )

Radius of organelles = Diameter / 2 =( 860) / 2 nm = 4.3 * 10^-7 m             (1 nm = 10^-9 m )

Volume of eukaryotic cell = (4/3)*π* r³ = (4/3)*π*(2.55 * 10^-5)³ m³ = 6.948 * 10^-14 m³

Volume of organelles = (4/3)*π* r³ = (4/3)*π*(4.3 * 10^-7)³ m³ = 3.331 * 10^-19 m³

No. of organelles cell can hold = Volime of eukaryotic cell / Volume of organelles

No. of organelles cell can hold = 6.948 * 10^-14 m³ / 3.331 * 10^-19 m³ = 208586