Question

AP Calculus:
The radius of a sphere is measured to be 3 inches. If the measurement is correct to within + or - .01 inch, use differentials to estimate the possible error in the volume of the sphere.

Answer 1

@Fall12-13 do you get how to do this?

Answer 2

No idea

Answer 3

@agent0smith do you know how to do this problem? :D

Answer 4

I can give it a shot

Answer 5

btw answer is \[\pm .36\pi \]

Answer 6

Alright. You can probably also check the answer just by putting r=3.01 and r=2.99 inches into the equation for volume of a sphere, it should give a similar figure.

Sphere volume:
\[V=\frac{ 4 }{ 3 }\pi r ^{3}\]
I think we just want to find dV/dr and then use dr as 0.01 inches and find dV...
\[\frac{ dV }{ dr }=4 \pi r ^{2}\]

Answer 7

Yeah that's all we need to do, it's actually kinda easy. Now we have dV/dr we can treat it as a fraction with dr = 0.01 inches, and find dV which will be the error in volume.
\[dV=4\pi r ^{2} dr\]

Answer 8

r = 3 inches and dr = +/- 0.01 inches, so substitute those in. For +0.01 you'll get dR = +0.36pi cubic inches, and for -0.01 you'll get dR = -0.36pi cubic inches. So dV = +/- 0.36pi cubic inches

Answer 9

ah ok ty <333

Answer 10

@agent0smith can you help me with another one please? :)

Answer 11

yeah probably