The cross-section of a sphere is a circle . The area of a circle can be calculated by the formula A= [tex] \pi\r^{2} [/tex] Where r is the radius of the circle.
Given :[tex] \pir^{2} = 100\pi [/tex]
Solving for r we have:
[tex] r^{2} = \frac{100\pi }{\pi}= 100 [/tex]
Or r= 10.
The area of a sphere is calculated by the formula :
[tex] SA = 4\pi R^{2} [/tex]
Substituting r value we have:
SA= [tex] 4\pi\ 10 ^{2} = 400\pi [/tex]
The total surface area of this sphere is 400π .
