1.
The cross-section of largest area is obtained when the cross-sectional plane, contains the center of the sphere.
That is, when this plane divides the sphere into 2 semi (half) spheres.
2.
This cross sectional region is a circle with surface area = 100 Pi square miles.
The area of a circle is [tex] \pi R^{2} [/tex], where R is the radius.
So
[tex]\pi R^{2}=100 \pi [/tex] square miles,
3.
The surface area of a sphere is given by the formula [tex]4\pi R^{2}[/tex]
So the surface area of this sphere is [tex]4\pi R^{2}=4*100 \pi =400 \pi [/tex] square miles.
Answer: [tex]400 \pi[/tex] square miles
