The radius of a 12 inch right circular cylinder is measured to be 4 inches, but with a possible error of ±0.2 inch. What is the resulting possible error in the volume of the cylinder? Include units in your answer.
Please explain in detail!
I know that V = pir^2h
r = 4 and h = 12
V = pi(4^2)(12) = 603.186
Given: r = radius = 4 h = height = 12 dr = error in radius = 0.2
What we want to find dV = error in volume
Use the derivative to find the differential dV V = pi*r^2*h dV/dr = d/dr[ pi*r^2*h ] dV/dr = 2pi*r*h dV = 2pi*r*h*dr dV = 2pi*4*12*0.2 dV = 19.2pi
So if the error in measuring the radius is +-0.2 inches, then the error in the cylinder volume is +-19.2pi cubic inches (we either measure the volume to be 19.2pi cubic inches too big, or 19.2pi cubic inches too small)
