Final answer:
When the radius of a sphere is halved, its surface area becomes one-fourth of the original surface area. The new surface area of the cell when its radius becomes r0/2 is πr0^2.
Step-by-step explanation:
If we model a cell as a sphere with radius r0, it has a surface area a0. To find the new surface area when the size of the cell changes such that its radius becomes r0/2, we need to calculate the new surface area a1.
The surface area of a sphere can be calculated using the formula a = 4πr^2, where a is the surface area and r is the radius.
Now, if the original radius is r0 and the new radius is r0/2, we substitute these values into the formula to calculate the new surface area:
a1 = 4π(r0/2)^2 = 4π(r0^2/4) = πr0^2
Therefore, the new surface area of the cell is a1 = πr0^2.
Learn more about Surface area of a sphere