The area of the surface of a sphere of radius r is 4πr^2. If the estimate radius of a spherical balloon is 200 meter and this estimate is too small by 1/2 meter. Find the approximate surface area in sq. m.

Answer 1

dA = 8πr dr
dr = -1/2, so
dA = 8π*200*(-1/2) = -800π m^2

so, the area is approximately

4π*200^2 - 800π = 159200π