Mathematics
Mathematics
Problem
Use the differential formulas in this chapter to solve these problems. The answers are in Chapter 19. 6. A cylindrical tank is constructed to have a diameter of 5 meters and a height of 20 meters. Find the error in the volume if (a) the diameter is exact, but the height is 20.1 meters; and (b) the height is exact, but the diameter is 5.1 meters.Intuitive explanation
The key here is using differentials to approximate small errors in a formula. Rather than computing exact volumes and subtracting, you'll use to estimate how a small change in one dimension ripples through to change the total volume. For a cylinder, , so take the differential with respect to whichever dimension changes, then plug in the given values and small changes to find the error.
Intuitive explanation
The key here is using differentials to approximate small errors in a formula. Rather than computing exact volumes and subtracting, you'll use to estimate how a small change in one dimension ripples through to change the total volume. For a cylinder, , so take the differential with respect to whichever dimension changes, then plug in the given values and small changes to find the error.