How Accurate Are Calculations of Circle Area and Sphere Volume?

[iRaid]

I have 2 problems that I'm wondering if they're right or not... Thanks for the help.

Homework Statement

10) What is the area, and its approximate uncertainty, of a circle of radius 3.8 x 10⁴cm?

Homework Equations

A=πr²

The Attempt at a Solution

A=π38000²
A=4536459792cm²
Then, I did the same thing with 37999 (the uncertainty is $$\pm$$ 1) to find the difference in the area to be 238758.
$$238758/4536459792$$ x 100% = .0053% uncertainty.

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Homework Statement

11) What, roughly, is the percent uncertainty in the volume of a spherical beach ball whose radius is r=2.86$$\pm$$0.09m?

Homework Equations

A=$$4/3$$πr³

The Attempt at a Solution

A=$$4/3$$π2.86³
A=97.99m³
I then did the same thing with 2.77 to get that area to be 89.03m³.
97.99-89.03=8.96
$$8.96/97.99$$x100%=9% uncertainty.

 

[anathema]

Hello,

Thank you for reaching out for help with your problems. I'm happy to assist you!

For problem 10, your solution looks correct. The area of a circle with a radius of 3.8 x 10^4 cm is approximately 4.536 x 10^9 cm^2. And your calculation for the percent uncertainty is also correct.

For problem 11, your solution is also correct. The volume of a sphere with a radius of 2.86 m is approximately 97.99 m^3 and the volume with a radius of 2.77 m is approximately 89.03 m^3. The difference in volumes is 8.96 m^3 and the percent uncertainty is 9%.

Great job on both problems! Keep up the good work. If you have any further questions or need clarification, please let me know.