Answer:
dA(s) = 22,917 cm² maximum error
dA(s) /A(s) = 0,01389 or 1,38 % relative error
Step-by-step explanation:
The Volume of a sphere is:
V(s) = 4/3)*π*r³ where r is the radius of circumference
If the length of circumference is 72 cm then
L (c) = 72 = 2*π*r
r = 72/2*π
r = 72/ 6,28 ⇒ r = 11,46 cm
And
L(c) = 2*π*r
Differentiation on both sides of the equation give:
dL (c) = 2*π*dr
dr = dL(c) /2*π
dr = 0,5 / 6,28 ⇒ dr = 0,07961
The surface area Is:
A (s) = 4*π*r²
And the maximum or absolute error is
dA(s) = 8*π*r*dr
dA(s) = 22,917 cm²
The relative error is dA(s) /A(s)
dA(s) /A(s) = 8*π*r*dr/ 4*π*r²
dA(s) /A(s) = 2*(0,07961)/ (11,46)
dA(s) /A(s) = 0,01389 or 1,38 %
