Question

A barn is an atomic unit of area equal to 10–28 m2. what is the surface area of the earth expressed in units of barn? assume the earth is a sphere with a radius of km. (the surface area of a sphere is 4πr2.)​

Answer 1

the complete question in the attached figure

we know that
surface area of a sphere=4*pi*r²
for r=6380 km------->r=6380 x 10^3 m

surface area of of the earth=4*pi*(6380 x 10^3)²-----> 511506576035121,52 m²

if 1 barn is equal to-------------> 10^(-28) m²
x barn----------------------> 511506576035121,52 m²
x=511506576035121,5/(10^(-28))------> x=5.12 x 10^42 barn

the answer is5.12 x 10^42 barn