The length of wire is 25.5cm and it's radius is 1.02mm. Calculate the percentage error in mesurement of its volume
Nothing
To calculate the percentage error in the measurement of the wire's volume, we need to determine the actual volume and the measured volume, and then calculate the percentage difference between them.
The formula for calculating the volume of a wire is V = πr^2h, where r is the radius and h is the length.
Given:
Length of wire = 25.5 cm
Radius of wire = 1.02 mm
To calculate the volume, we need to convert the length and radius to the same unit. Converting the length from cm to mm:
Length of wire = 25.5 cm * 10 = 255 mm
Calculating the actual volume:
Actual Volume = π * (1.02 mm)^2 * 255 mm
Now, let's calculate the measured volume:
Measured Volume = π * (1.02 mm ± error)^2 * 255 mm
To calculate the percentage error, we need to subtract the measured volume from the actual volume, divide by the actual volume, and multiply by 100.
Percentage Error = (Measured Volume - Actual Volume) / Actual Volume × 100
Now, let's calculate the actual and measured volume:
Actual Volume = π * (1.02 mm)^2 * 255 mm
≈ 3.1416 * (1.02 mm)^2 * 255 mm
≈ 824.47 mm^3
Measured Volume = π * (1.02 mm ± error)^2 * 255 mm
Now, let's calculate the upper and lower bound for the measured volume. Considering the given radius error is ± 1.02 mm:
Upper Bound Measured Volume = π * (1.02 mm + 1.02 mm)^2 * 255 mm
= π * (2.04 mm)^2 * 255 mm
Lower Bound Measured Volume = π * (1.02 mm - 1.02 mm)^2 * 255 mm
= π * (0 mm)^2 * 255 mm
= 0 mm^3
Now, let's calculate the percentage error:
Upper bound Percentage Error = (Upper Bound Measured Volume - Actual Volume) / Actual Volume × 100
Lower bound Percentage Error = (Lower Bound Measured Volume - Actual Volume) / Actual Volume × 100
The percentage error in measurement of its volume can be calculated as the average of the upper and lower bound percentages:
Percentage Error = (Upper bound Percentage Error + Lower bound Percentage Error) / 2
Please note that you need to replace the ± symbol with the exact value of the error given in your question to get accurate calculations.
To calculate the percentage error in the measurement of the volume, you need to compare the actual value of the volume with the measured value.
First, let's calculate the actual volume of the wire.
The formula for the volume of a cylindrical wire is given by:
V = πr^2h
Where:
V = volume
r = radius
h = height/length (in this case)
Given:
Length (h) = 25.5 cm
Radius (r) = 1.02 mm = 0.102 cm (since 1 cm = 10 mm)
Substituting the values into the formula, we have:
V = π * (0.102)^2 * 25.5
Now, we can calculate the actual volume using a calculator:
V ≈ 0.082 cm^3 (rounded to three decimal places)
Next, let's calculate the measured volume. Since we have been given the length and radius, we can just use the same formula as above, but with the measured values:
Measured Length (h) = 25.5 cm (same as given)
Measured Radius (r) = 1.02 mm = 0.102 cm (same as given)
Substituting these values:
Measured V = π * (0.102)^2 * 25.5
Now, we can calculate the measured volume using a calculator:
Measured V ≈ 0.082 cm^3 (rounded to three decimal places)
Now, we can calculate the percentage error in measurement:
Percentage Error = |(Actual V - Measured V) / Actual V| * 100
Substituting the actual and measured volumes into the formula, we have:
Percentage Error = |(0.082 - 0.082) / 0.082| * 100
Since both the actual and measured volumes are the same, the numerator of the expression becomes zero.
Therefore, the percentage error in the measurement of its volume is 0%.