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The diameter and height of a right circular cylinder are 3 cm and 4 cm, respectively. The absolute error in each of these two measurements is 0.2 cm. The absolute error in the computed volume (in cm3, round off to three decimal places), is _______.
Correct answer is '5.18'. Can you explain this answer?
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Verified Answer
The diameter and height of a right circular cylinder are 3 cm and 4 cm...
Let diameter, x = 3 and height = y = 4 and error = ± 0.2
∴ V = f (x, y )
So,
i.e.,
= 1.65 × 3.14 = 5.18 (approx)
i.e., absolute error = | 5.18 | = 5.18
∴ V = f (x, y )
So,
i.e.,
= 1.65 × 3.14 = 5.18 (approx)
i.e., absolute error = | 5.18 | = 5.18
Most Upvoted Answer
The diameter and height of a right circular cylinder are 3 cm and 4 cm...
Diameter and Height of the Cylinder:
Given that the diameter of the cylinder is 3 cm and the height is 4 cm.
Absolute Error:
The absolute error in each of these measurements is 0.2 cm.
Calculating the Computed Volume:
To calculate the volume of a right circular cylinder, we use the formula:
V = πr^2h
Calculating the Radius:
The radius can be calculated using the formula:
r = d/2
Substituting the given diameter into the formula, we get:
r = 3/2
r = 1.5 cm
Calculating the Volume:
Using the calculated radius and given height, we can calculate the volume of the cylinder:
V = π(1.5)^2(4)
V = 18π cm^3
Calculating the Absolute Error in Volume:
To calculate the absolute error in the computed volume, we need to consider the effect of absolute errors in both the radius and height.
Effect of Absolute Error in Radius:
The error in the radius is 0.2 cm. This means that the actual radius could be 1.5 cm + 0.2 cm or 1.5 cm - 0.2 cm.
Maximum Radius:
The maximum radius will be:
1.5 cm + 0.2 cm = 1.7 cm
Minimum Radius:
The minimum radius will be:
1.5 cm - 0.2 cm = 1.3 cm
Effect of Absolute Error in Height:
The error in the height is also 0.2 cm. This means that the actual height could be 4 cm + 0.2 cm or 4 cm - 0.2 cm.
Maximum Height:
The maximum height will be:
4 cm + 0.2 cm = 4.2 cm
Minimum Height:
The minimum height will be:
4 cm - 0.2 cm = 3.8 cm
Calculating the Maximum Volume:
Using the maximum values for radius and height, we can calculate the maximum volume:
V_max = π(1.7)^2(4.2)
Calculating the Minimum Volume:
Using the minimum values for radius and height, we can calculate the minimum volume:
V_min = π(1.3)^2(3.8)
Calculating the Absolute Error in Volume:
The absolute error in volume is the difference between the maximum and minimum volumes:
Absolute Error = V_max - V_min
Substituting the values and rounding off to three decimal places, we get:
Absolute Error = 5.18 cm^3
Therefore, the absolute error in the computed volume is 5.18 cm^3.
Given that the diameter of the cylinder is 3 cm and the height is 4 cm.
Absolute Error:
The absolute error in each of these measurements is 0.2 cm.
Calculating the Computed Volume:
To calculate the volume of a right circular cylinder, we use the formula:
V = πr^2h
Calculating the Radius:
The radius can be calculated using the formula:
r = d/2
Substituting the given diameter into the formula, we get:
r = 3/2
r = 1.5 cm
Calculating the Volume:
Using the calculated radius and given height, we can calculate the volume of the cylinder:
V = π(1.5)^2(4)
V = 18π cm^3
Calculating the Absolute Error in Volume:
To calculate the absolute error in the computed volume, we need to consider the effect of absolute errors in both the radius and height.
Effect of Absolute Error in Radius:
The error in the radius is 0.2 cm. This means that the actual radius could be 1.5 cm + 0.2 cm or 1.5 cm - 0.2 cm.
Maximum Radius:
The maximum radius will be:
1.5 cm + 0.2 cm = 1.7 cm
Minimum Radius:
The minimum radius will be:
1.5 cm - 0.2 cm = 1.3 cm
Effect of Absolute Error in Height:
The error in the height is also 0.2 cm. This means that the actual height could be 4 cm + 0.2 cm or 4 cm - 0.2 cm.
Maximum Height:
The maximum height will be:
4 cm + 0.2 cm = 4.2 cm
Minimum Height:
The minimum height will be:
4 cm - 0.2 cm = 3.8 cm
Calculating the Maximum Volume:
Using the maximum values for radius and height, we can calculate the maximum volume:
V_max = π(1.7)^2(4.2)
Calculating the Minimum Volume:
Using the minimum values for radius and height, we can calculate the minimum volume:
V_min = π(1.3)^2(3.8)
Calculating the Absolute Error in Volume:
The absolute error in volume is the difference between the maximum and minimum volumes:
Absolute Error = V_max - V_min
Substituting the values and rounding off to three decimal places, we get:
Absolute Error = 5.18 cm^3
Therefore, the absolute error in the computed volume is 5.18 cm^3.
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The diameter and height of a right circular cylinder are 3 cm and 4 cm, respectively. The absolute error in each of these two measurements is 0.2 cm. The absolute error in the computed volume (in cm3, round off to three decimal places), is _______.Correct answer is '5.18'. Can you explain this answer?
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