cant get the answer for this question and all the working in between!-rates of change (1 Viewer)

[Lil Clutch]

can someone help please?
im just revising rates of change and cant get out this question from "understanding year 12 maths" textbook, dr max shur,page 206

question: a circular metal plate of radius r is heated so that its area expands at a constant rate of 4cm^2/min. at what rate does the radius increas wen r= 10cm.

its a hell easy question! its the first one! and like i do other questions similar to this, but i do generally suck at rates of change and hence cant do this question.

help is much appreciated! but i will turn to my teachers as well! jsut most of the time i understand this internet help over my particular maths teacher. now i wont blame her!

 

[KFunk]

The rate of change of area with respect to time:
dA/dt = 4

The rate of change of area with respect to radius:
A = πr²
hence dA/dr = 2πr -----> dr/dA = 1/(2πr)

dr/dt = dA/dt . dr/dA = 4. 1/(2πr) = 2/(πr)

so given that dr/dt = 2/(&pi;r) ---> when r=10, dr/dt = 2/(10&pi; ) = 0.064 cm/min <--EDIT [You should include units ]

 

[Lil Clutch]

why thank you very much! all makes sense now