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.
r = 4 in.
h = 12 in.
V = pi*r^2 * h = 3.14*4^2 * 12 = 602.88
m^3.
r = 4.2 in.
h = 12.2 in.
V = 3.14*4.2^2 * 12.2 = 675.75 in^3
Error = 675.75 - 602.88 = 72.87 in^3
To find the resulting possible error in the volume of the cylinder, we first need to calculate the volume of the cylinder using the radius of 4 inches.
The volume of a right circular cylinder can be calculated using the formula:
V = π * r^2 * h
Where:
V = Volume of the cylinder
π = Pi (approximately 3.14159)
r = Radius of the cylinder
h = Height of the cylinder
In this case, the radius of the cylinder is given as 4 inches, so we can substitute the values into the formula:
V = π * (4^2) * h
Now, we need to find the resulting possible error in the volume. We know that the radius has a possible error of ±0.2 inches.
To find the upper bound of the radius, we add the possible error to the radius:
Upper bound = 4 + 0.2 = 4.2 inches
To find the lower bound of the radius, we subtract the possible error from the radius:
Lower bound = 4 - 0.2 = 3.8 inches
Now, we need to calculate the volume using the upper and lower bounds of the radius.
Calculating the volume with the upper bound of the radius:
V_upper = π * (4.2^2) * h
Calculating the volume with the lower bound of the radius:
V_lower = π * (3.8^2) * h
The resulting possible error in the volume of the cylinder can be found by subtracting the lower bound volume from the upper bound volume:
Possible error = V_upper - V_lower
Once you have substituted the values and calculated this expression, you will get the answer in cubic inches, which will be the resulting possible error in the volume of the cylinder.