Question

the area of the cross section of a sphere at the largest point is 100 Pi square miles. What is the total surface area of the sphere?

Answer 1

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
`\pi R^(2)`, where R is the radius.

So


`\pi R^(2)=100 \pi` square miles,

3.

The surface area of a sphere is given by the formula
`4\pi R^(2)`

So the surface area of this sphere is
`4\pi R^(2)=4*100 \pi =400 \pi` square miles.


Answer:
`400 \pi` square miles