SOLUTION: The altitude of a certain circular cone is the same as the radius if the base is measured as 12 cm with a possible error of 0.04 cm. Find the approximate percentage error in th

Algebra ->  Bodies-in-space -> SOLUTION: The altitude of a certain circular cone is the same as the radius if the base is measured as 12 cm with a possible error of 0.04 cm. Find the approximate percentage error in th      Log On


   

Question 1082949: The altitude of a certain circular cone is the same as the radius
if the base is measured as 12 cm with a possible error of 0.04 cm.
Find the approximate percentage error in the calculated value of
the volume.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for the volume of a cone is

V=expr%281%2F3%29pi%2Ar%5E2%2Ah

Since the altitude is the same as the radius, we
substitute h=r

V=expr%281%2F3%29pi%2Ar%5E2%2Ar

V=expr%281%2F3%29pi%2Ar%5E3

dV%2Fdr=expr%281%2F3%29%283r%5E2%29

dV%2Fdr=r%5E2%29

dV=r%5E2%2Adr

Substitute the possible error in the base for dr,
and 12 for r:

dV=12%5E2%2A%28%22%22+%2B-+0.04%29

dV=%22%22+%2B-+matrix%281%2C3%2C5.76%2Ccubic%2Ccentimeters%29  <-- approximate error in the volume.

To find the approximate percentage error, we find what the
actual volume should be:

V=expr%281%2F3%29pi%2Ar%5E3
V=expr%281%2F3%29pi%2A12%5E3
V=matrix%281%2C3%2C1809.557368%2Ccubic%2Ccentimeters%29

We find what percent 5.76 cubic centimeters is of that,
we calculate 5.76%2F1809.557368+=+0.0031830989=%220.31830989%25%22

Edwin