Please help with this question to do with accuracy!
The volume of a square pyramid is given by (b^2)h=3. If the base size b and the height h can be measured with an accuracy of 1%, how accurately can the volume be determined? State what assumptions you make.
Accuracy Question
2008-04-01 3:12 am
回答 (1)
2008-04-04 3:09 am
✔ 最佳答案
Since volume V = (1/3)b^2.hdifferentiate on both sides,
dV = (1/3)[b^2.dh + 2b.h.db]
dividing by V on both sides,
dV/V = (1/3)[b^2.dh + 2b.h.db]/V
i.e. dV/V = (1/3)[b^2.dh+ 2b.h.db]/[(1/3)(b^2.h]
dV/V = dh/h + 2(db/b)
since dh/h = db/b = 0.01 (i.e. 1%)
hence, dV/V = 0.01 + 2x0.01 = 0.03
or dV = 0.03V
therefore, the volume is of 3% uncertainty
收錄日期: 2021-05-01 19:08:42
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080331000051KK02014