The radius of a 10 inch right circular cylinder is measured to be 4 inches, but with a possible error of ±0.1 inch. use linear approximation or differentials to determine the possible error in the volume of the cylinder.

±13 in³  

Step-by-step explanation:

V =πr²h

Take differentials of each side.

dV = πrhdr

ΔV = πrhΔr

Data:

  r =   4 in

 h = 10 in

Δr = 0.1 in

Calculation

ΔV = πrhΔr = π × 4 in × 10 in × 0.1 in = 4π in³ ≈ 13 in³

The possible error in the volume of the cylinder is ±13 in³

the answer is 99.