Solve the Problem $S = 2 \pi \left( R _ { 1 } + R _ { 2 } \right) \left( h + R _ { 1 } - R _ { 2 } \right) ,$

Multiple Choice

Solve the problem.
-The surface area of a hollow cylinder (tube) is given by $S = 2 \pi \left( R _ { 1 } + R _ { 2 } \right) \left( h + R _ { 1 } - R _ { 2 } \right) ,$ where $\mathrm { h }$ is the length of the cylinder and $\mathrm { R } _ { 1 }$ and $\mathrm { R } _ { 2 }$ are the outer and inner radii. If $\mathrm { h } _ { , } \mathrm { R } _ { 1 }$ , and $\mathrm { R } _ { 2 }$ are measured to be 10 inches, 3 inches, and 5 inches respectively, and if these measurements are accurate to within $0.1$ inches, estimate the maximum possible error in computing $S$ .

A) 15.08
B) 16.96
C) 11.31
D) 13.19