00:01
For this problem, we are told that the radius of a spherical ball is measured at r equals 25 centimeters.
00:06
We are asked to estimate the maximum error in the volume and surface area if r is accurate to within 0 .5 centimeters.
00:14
So let's begin with the volume.
00:15
We know that the volume of a sphere is 4 over 3 times pi r cubed.
00:21
So we are going to need the second derivative volume for this.
00:25
So the first derivative is going to be 4 times pi r squared.
00:29
And the second derivative is going to be 8 times pi times r.
00:37
So we want to have the maximum, we want, excuse me, one second here, we want to determine what the maximum of the second derivative will be in the interval from 25 up to 25 .5 and down to 24 .5 rather.
00:56
So obviously that's going to be at 25 .5.
01:01
And so i'm going to pause for a second and calculate that off screen...