Calculating the Volume of a Cylinder with Uncertainty

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In summary, the volume of the beaker is 604.48 ± 35.6 cm^3 and the sum of the 4 glasses is 1000cm^3. The beaker is not large enough to hold the 4 glasses of liquid.
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123webfkebf
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Homework Statement


4 glasses of liquid must be transfferred into a beaker that has a cylinder shape without any markings. The teacher says that the glass will hold 250mL, but the uncertainty was 10mL in which this was determined. The radius and the height of the beaker was measured within an accuracy of 0.5cm, where

radius = 4 ± 0.1cm
height to the rim= 20 ± 0.5cm

Will the 4 glasses of liquid be poured into the beaker?

Show your work, and explain.


Homework Equations


N/A


The Attempt at a Solution


find the volume of the beaker using v=pi(r^2), and then compare it to the sum of the 4 glasses?
 
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  • #2
The volume of the beaker is: v=pi(r^2)hv= 3.14(4 ± 0.1)^2(20 ± 0.5) v= 3.14(16 ± 0.4)(20 ± 0.5) v= 604.48 ± 35.6 cm^3The sum of the 4 glasses is: 4 * 250mL = 1000mL1000mL = 1L1L = 1000cm^3Therefore, the sum of the 4 glasses is 1000cm^3. Since the volume of the beaker is 604.48cm^3, it is not large enough to hold the 4 glasses of liquid.
 

1. How do you calculate the volume of a cylinder with uncertainty?

To calculate the volume of a cylinder with uncertainty, you need to use the formula V = πr²h, where V is the volume, π is a constant equal to approximately 3.14, r is the radius, and h is the height. To account for uncertainty, you will need to calculate the upper and lower bounds of each variable and plug them into the formula to get a range of possible volumes.

2. What is the formula for uncertainty in volume calculation?

The formula for uncertainty in volume calculation is ΔV = πΔr²h + πr²Δh, where ΔV is the uncertainty in volume, Δr is the uncertainty in radius, and Δh is the uncertainty in height. This formula takes into account the uncertainty in each variable and gives an overall uncertainty in the volume calculation.

3. How do you determine the uncertainty in the radius and height of a cylinder?

The uncertainty in the radius and height of a cylinder can be determined through measurement error or by using a calibrated measuring tool. The uncertainty will depend on the precision and accuracy of the measurement and can be expressed as a percentage or absolute value.

4. Can the uncertainty in volume be reduced?

Yes, the uncertainty in volume can be reduced by improving the precision and accuracy of the measurements for the radius and height. This can be done by using more precise measuring tools or taking multiple measurements and averaging them. The uncertainty can also be reduced by using a larger sample size.

5. How does uncertainty affect the calculated volume of a cylinder?

Uncertainty in the measurements used to calculate the volume of a cylinder can cause the final volume to have a range of possible values, rather than a single definite value. The larger the uncertainty, the wider the range of possible volumes will be. It is important to consider and report the uncertainty to accurately represent the precision and reliability of the calculated volume.

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