we know that
The circumference is
70.000 ± 0.500
so
C=70.500 or C=69.500
step 1
Find out the radius of the sphere
[tex]C=2\pi r[/tex]
For C=70.500
[tex]\begin{gathered} 70.500=2\pi r \\ r=\frac{70.500}{2\pi} \\ r=11.220 \end{gathered}[/tex]
For C=70.000
[tex]\begin{gathered} 70.000=2\pi r \\ r=\frac{70.000}{2\pi} \\ \\ r=11.141 \end{gathered}[/tex]
step 2
Find out the surface area
For r=11.220
[tex]\begin{gathered} SA=4\pi r^2 \\ SA=4\pi(\frac{70.50}{2\pi})^2 \\ SA=1,582.882 \end{gathered}[/tex]
For r=11.141
[tex]\begin{gathered} SA=4\pi(\frac{70.000}{2\pi})^2 \\ SA=1,560.510 \end{gathered}[/tex]
The maximum error is given by the difference
1,582.882-1,560.510=22.372
