求助！Add maths differentiation~!!

[复制链接]

paopaoyuu

2012-10-13 03:41 PM

the surface area of a sphere increases at the rate of 20cm square/s. find the rate of change of its volume when the radius is 15cm.

要找 dV/dt
有：
dA/dt = 20
r= 15

答案是150cm cube/ s

Soo_135

2012-10-13 04:23 PM

回复 1# paopaoyuu

资料：
  V =  (4/3 ) π r^3
  dV / dr = 4 π r^2

A=4 π r^2
dA / dr = 8π r

做法：
dV / dt = (dr / dt ) X  ( dV / dr )
         = ( 不懂，要找）  X ( 4 π r^2)

所以就找咯：
dA / dt = ( dr / dt ) X ( dA/ dr)
  20    = ( dr / dt )  X  8 π r
dr / dt  = 20  X 1 /  ( 8π ( 15)  )
         =  20 X 1 /  ( 120 π)
         = 1 / (6 π )

最后丢完全部进去：
dV / dt = (dr / dt ) X  ( dV / dr )
         =  1 / (6π)  X ( 4 π r^2)
         = 1/ (6π) X 4 π (15)(15)
         =150