Question

Assume that a spherical cell, with a diameter of 23 μm, has spherical mitochondria, each with a diameter of 0.23 μm. If mitochondria occupy 17.7% of the volume of the cell, how many mitochondria are there?

Answer 1

Total number of mitochondria
`= 177000`

Step-by-step explanation:

Given ,

Diameter of spherical cell
`= 23`μm

Diameter of spherical mitochondria
`= 23`μm

Total volume of spherical cell

`(4)/(3) \pi (23)^(3)`

Volume of cell occupied by mitochondria

`(17.7)/(100)* (4)/(3) \pi (23)^3`

Number of mitochondria

`((17.7)/(100)*(4)/(3)*\pi*((23)/(2) )^3  )/((4)/(3)*\pi*((0.23)/(2) )^3) \\= 177000`

Total number of mitochondria
`= 177000`