The radius of a sphere is in error a maximum of 4%. Use differentials to estimate the maximum error in the surface area of the sphere. - any help would be greatly appreciated. Thanks!!
2007-07-04 21:06:52 · 4 answers · asked by Nicholas T 2 in Science & Mathematics ➔ Mathematics
A = 4*pi * r^2
lnA = ln(4pi) + 2ln(r)
taking differentials as errors
(dA /A) = 0 + 2 (dr / r)
multiply by 100
(dA /A)*100 = 2 (dr / r)*100
(dA /A)*100 = 2 *4 = 8 %
+ or - 8% would be a better answer
2007-07-04 21:18:48 · answer #1 · answered by qwert 5 · 0⤊ 1⤋
The surface area of a sphere is
S=4*pi*r^2
take the derivative with respect to r...
dS=8*pi*r*dr
now dr is the differential which is 4% or 0.04 plus or minus...
dS=8*pi*r*(+/- 0.04)
= +/- 0.32*pi*r
2007-07-05 04:21:46 · answer #2 · answered by manish.narayan 3 · 0⤊ 1⤋
i can't tell you to solve this with differentials, however, i would take the folowing aproach:
you take the formula for the surface area of the sfere and replace the radius R once with 1.04*R abd again with 9.6*R.
you do the calcules, and you'll get 2 results, both representing the minimum and maximum value you get for the surface area.
2007-07-05 04:12:42 · answer #3 · answered by fesoj 1 · 0⤊ 1⤋
S=4pir^2 = surface area
dS/dr= 8pir
dS= 8pirdr
dr = +/- .04r
dS=
dS = 8pir(+/-.04r)= +/- .32pir^2
2007-07-05 11:16:41 · answer #4 · answered by ironduke8159 7 · 0⤊ 0⤋