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.
nominal ... π * 4^2 * 12
max ... π * 4.2^2 * 12
min ... π * 3.8^2 * 12
units are in^3
If we apply linear approximation using calculus, then:
V=πr^2h
dV/dr=2πrh
ΔV≈2πrhΔr
=2π(4)(12)(+0.2-(-0.2))
=2π(4)(12)(0.4)
=38.4π
To calculate the error in the volume of the cylinder, we first need to calculate the actual volume and then the maximum and minimum possible volumes.
The volume of a right circular cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
Given that the radius is measured to be 4 inches with a possible error of ±0.2 inches, the maximum radius would be 4 + 0.2 = 4.2 inches, and the minimum radius would be 4 - 0.2 = 3.8 inches.
Assuming the height remains constant, we can calculate the maximum and minimum possible volumes:
Maximum volume = π(4.2)^2h = 22.176h cubic inches
Minimum volume = π(3.8)^2h = 18.144h cubic inches
The resulting possible error in the volume of the cylinder is the difference between the maximum and minimum volumes:
Possible error in volume = Maximum volume - Minimum volume
= 22.176h - 18.144h
= 4.032h cubic inches
The units for the possible error in the volume are cubic inches.
Note: Since the height of the cylinder is not given or specified, we cannot determine the exact value for the error in the volume. However, the answer provided above gives you a general idea of how to calculate the possible error in the volume of the cylinder when the radius has an error range of ±0.2 inches.