What is the percent uncertainty in the volume of a spherical beach ball whose radius is r = 2.86 +/- 0.09m?

Question

any help appreciated thanks in advance

Answer 1

Use differential calculus...

dV = 4*PI*R^2*dR  so dV = 4*3.141592...* 2.86^2 * .09 = 9.3 (approx.)

.102/V where V = 4/3 PI R^3 and R = 2.88 = 97.99

So the % uncertainty is 9.3/97.99 * 100 = 9.5%

You may also "brute force" it...

Take 4/3 PI (2.95^3-2.86^3) and compare to 97.99, but the calculus method is generally prefered.

-Fred