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

Question

Quizplus · Accepted Answer

The maximum possible error in computing $S$ is the sum of the absolute values of the errors in measuring $h$, $R_1$, and $R_2$. So, the maximum possible error is $0.1 + 0.1 + 0.1 = 0.3$ inches. The maximum possible error in computing $S$ is then $0.3 \times 2 \pi \left( 3 + 5 \right) \left( 10 + 3 - 5 \right) = 15.08$ square inches.

Solve the Problem S=2π(R1+R2)(h+R1−R2),S = 2 \pi \left( R _ { 1 } + R _ { 2 } \right) \left( h + R _ { 1 } - R _ { 2 } \right) ,S=2π(R1​+R2​)(h+R1​−R2​),

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