Question

As the new cell grows, its plasma membrane needs to expand to contain the increased volume of the cell. (a) Calculate the surface area of each cell using the formula for the surface area of a sphere: \({\rm{A}} = 4{\rm{\pi }}{{\rm{r}}^2}\). (b) How much area of new plasma membrane will the new cell have to synthesize as its matures?

Short answer

(a) The surface area of the mature cell is 50µm^2, and the surface area of the new cell is 28µm².

(b) The new cell needs 22µm²more plasma membrane area to form a mature cell.

Step-by-step solution

Description of the surface area of the sphere

The surface area of the sphere is calculated using the mathematical expression\(4{\rm{\pi }}{{\rm{r}}^2}\). In this formula, r is the radius used to predict the surface area of the sphere.

The yeast cells are irregularly shaped cells that are approximated as a sphereto predict its surface area.

Surface area of the parent cell

The diameter of the parent cell is 4µm; thus, its radius is 2µm.

The surface area of the parent cell or matured cell = \(4{\rm{\pi }}{{\rm{r}}^2}\)

=\(4 \times 3.14 \times {2^2}\)

= \(50{\rm{\mu }}{{\rm{m}}^2}\)

Surface area of the budding cell

The diameter of the budding cell is 3µm; thus, its radius is 1.5µm.

The surface area of the budding cell = \(4{\rm{\pi }}{{\rm{r}}^2}\)

=\(4 \times 3.14 \times {1.5^2}\)

= \(28{\rm{\mu }}{{\rm{m}}^2}\)

Difference between the surface area of the parent cell and the budding cell

The required surface area for the budding cell to form a mature cell is calculated by subtracting the budding cell's surface area from the parent cell's surface area.

\({\rm{Difference}}\,{\rm{ = }}\,{\rm{50\mu }}{{\rm{m}}^{\rm{2}}}{\rm{ - }}\,{\rm{28\mu }}{{\rm{m}}^2}{\rm{ = 22\mu }}{{\rm{m}}^{\rm{2}}}\)