1.Sand pouring from a bucket forms a conical pile whose diameter is alwats three times its altitude. The base radius is inceasing at 1/8 cm/s when it is 12cm.Find the rate of change of the bolume at this instant.
Ans:12派cm3/s
applications of differentiation
2007-10-08 1:30 am
回答 (1)
2007-10-08 1:39 am
✔ 最佳答案
As given, 2r = 3h
h = 2r / 3
V = πr^2h / 3
= πr^2 ( 2r / 3 ) / 3
= 2πr^3 / 9
dV / dt = ( 2π/ 9 )( 3r^2 )( dr / dt )
dV / dt = ( 2π / 9 )( 3 )( 12^2 )( 1 / 8 )
dV / dt = 12π
So the rate of change of volume is 12πcm^3/s.
參考: My Maths Knowledge
收錄日期: 2021-04-13 13:48:34
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