PLEASE help me with this question! I am really stuck...

8π cm^2

Step-by-step explanation:

We proceed as follows;

To answer this question, what we need firstly is the name of the cross section that results from slicing a sphere into half.

The cross section that results is called a hemisphere, which is half the size of the sphere.

But before we can calculate the area of the new cross section, we will need the radius of the original shape.

This is obtainable from the volume of the shape.

Mathematically;

Volume of a sphere = 4/3 * π * r^3

32/3 * π = 4/3 * π * r^3

We can take off π/3 from both sides so we are left with;

32 = 4r^3

Divide through by 4

r^3 = 8

r is the cube root of 8 = 2 cm

Now we find the area of the hemisphere

Mathematically, the area of a hemisphere is 2 * π * r^2

using the value of r = 2 cm given above, we have Hemisphere area = 2 * π * 2^2 =8 π cm^2