ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: GoodGuys on October 07, 2009, 07:29:38 pm

Title: question.
Post by: GoodGuys on October 07, 2009, 07:29:38 pm: Water is filling a cylinder which has a radius of 5cm. The height of the water in the cylinder is changing at the variabel rate of 1/T cm / sec. The rate, in cm cube / sec, at which the volume of the water in the cylinder is changing at T = 10 secs is?

Thankssss!!!!
Title: Re: question.
Post by: TrueTears on October 07, 2009, 07:35:56 pm: $V = \pi r^2h$

$r = 5$

$\frac{dV}{dh} = 25 \pi$ $cm^3/cm$

$\frac{dh}{dt} = \frac{1}{T}$ $cm/s$

$\frac{dV}{dt} = \frac{dV}{dh} \frac{dh}{dt} = 25 \pi (\frac{1}{10})$
Title: Re: question.
Post by: Flaming_Arrow on October 07, 2009, 07:39:15 pm: dh/dt = 1/T

dV/dt = dh/dt * dV/dh

V= pi r^2h
V= 25pi h
dV/dh = 25pi

dV/dt = 1/T * 25 pi

dV/dt = 1/10 * 25 pi
dV/dt = 5 pi /2 cm^3/s
Title: Re: question.
Post by: GoodGuys on October 07, 2009, 08:10:55 pm: Thanks bro.