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I'm stressing out because I can't work this math equation out! so my question is: How do you find the maximum percentage error of the volume of a cylinder if the radius is 3.5cm and the height is 12.2cm both to 1 decimal place?
Original post by HannahWilo
I'm stressing out because I can't work this math equation out! so my question is: How do you find the maximum percentage error of the volume of a cylinder if the radius is 3.5cm and the height is 12.2cm both to 1 decimal place?

What have you tried? You need to post some working as per forum guidelines :smile:
Original post by HannahWilo
I'm stressing out because I can't work this math equation out! so my question is: How do you find the maximum percentage error of the volume of a cylinder if the radius is 3.5cm and the height is 12.2cm both to 1 decimal place?


No need to stress out, here comes the answer and explanation:

To find the maximum percentage error of the volume of a cylinder, you will need to first determine the maximum possible error in the measurements of the radius and height. Since both the radius and height are measured to 1 decimal place, the maximum possible error in each measurement is 0.1 cm (1/10 of the smallest unit of measurement).

Next, you will need to calculate the volume of the cylinder using the given measurements of the radius and height, and then calculate the volume of the cylinder using the maximum possible error for each measurement. The difference between these two volumes will be the maximum possible error in the volume of the cylinder.

The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. Using the given measurements of r = 3.5 cm and h = 12.2 cm, the volume of the cylinder is V = π(3.5^2)(12.2) = 155.4 cm^3.

To find the maximum possible error in the volume of the cylinder, we will need to calculate the volume using the maximum possible error in the measurements of the radius and height. The maximum possible error in the radius is 0.1 cm, and the maximum possible error in the height is also 0.1 cm. Using these values, the volume of the cylinder is V = π(3.6^2)(12.3) = 167.3 cm^3.

The difference between these two volumes is 167.3 - 155.4 = 11.9 cm^3. This is the maximum possible error in the volume of the cylinder. To express this error as a percentage, we will need to divide the error by the volume of the cylinder and multiply by 100%.

The maximum percentage error in the volume of the cylinder is (11.9/155.4) * 100% = 7.7%.

I hope this helps! Let me know if you have any other questions.
Reply 3
Original post by Curious_Bilawi
No need to stress out, here comes the answer and explanation:




Er, do you think you could read the posting guidelines for this forum please? It is against forum rules to post full solutions! Please delete the details from your answer, thanks :smile:
Reply 4
Original post by Curious_Bilawi
No need to stress out, here comes the answer and explanation:

To find the maximum percentage error of the volume of a cylinder, you will need to first determine the maximum possible error in the measurements of the radius and height. Since both the radius and height are measured to 1 decimal place, the maximum possible error in each measurement is 0.1 cm (1/10 of the smallest unit of measurement).

Next, you will need to calculate the volume of the cylinder using the given measurements of the radius and height, and then calculate the volume of the cylinder using the maximum possible error for each measurement. The difference between these two volumes will be the maximum possible error in the volume of the cylinder.

The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. Using the given measurements of r = 3.5 cm and h = 12.2 cm, the volume of the cylinder is V = π(3.5^2)(12.2) = 155.4 cm^3.

To find the maximum possible error in the volume of the cylinder, we will need to calculate the volume using the maximum possible error in the measurements of the radius and height. The maximum possible error in the radius is 0.1 cm, and the maximum possible error in the height is also 0.1 cm. Using these values, the volume of the cylinder is V = π(3.6^2)(12.3) = 167.3 cm^3.

The difference between these two volumes is 167.3 - 155.4 = 11.9 cm^3. This is the maximum possible error in the volume of the cylinder. To express this error as a percentage, we will need to divide the error by the volume of the cylinder and multiply by 100%.

The maximum percentage error in the volume of the cylinder is (11.9/155.4) * 100% = 7.7%.

I hope this helps! Let me know if you have any other questions.


Thank you so much, it was very helpful :smile:

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