# derivative problem

• May 24th 2007, 06:33 AM
inolas_cul
derivative problem
assuming that the volume of the trunk is directly proportional to the cube of its diameter,and that the latter increases uniformly from year to year,show that the rate of increase in the volume when the diameter is equal to 90 cm is 25 times the rate when its 18cm.
• May 24th 2007, 07:54 AM
CaptainBlack
Quote:

Originally Posted by inolas_cul
assuming that the volume of the trunk is directly proportional to the cube of its diameter,and that the latter increases uniformly from year to year,show that the rate of increase in the volume when the diameter is equal to 90 cm is 25 times the rate when its 18cm.

$V = k d^3$

so:

$\frac{dV}{dt} = 3k d^2 \frac{d}{dt}d$

but $({d}/{dt}) d$ is constant, so

$
\frac{ dV/dt |_{d=90}}{ dV/dt |_{d=18}} = 90^2/18^2= 25
$

RonL