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.
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
To find the approximate surface area of the spherical balloon, we first need to correct the estimated radius by adding the discrepancy of 1/2 meter.
Corrected radius = Estimated radius + Discrepancy
= 200 m + 1/2 m
= 200.5 m
Now, we can use the formula for the surface area of a sphere to calculate the approximate surface area.
Surface area = 4πr^2
Substituting the corrected radius into the formula:
Surface area ≈ 4π(200.5)^2
Calculating this expression will give us the approximate surface area of the balloon in square meters.