logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  CBSE XII  >>  Math  >>  Application of Derivatives
0 votes

Find the rate of change of the area of a circle with respect to its radius r when $(a)\; r = 3 cm$

$\begin{array}{1 1} \;6 \pi\;cm^2/cm \\ 6 \pi m^2/cm \\ 6 \pi m/cm \\ 6 \pi cm^2 \end{array} $

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • If $y=f(x)$,then $\large\frac{dy}{dx}$ measures the rate of change of $y$ w.r.t $x$.
  • $\big(\large\frac{dy}{dx}\big)_{x=x_0}$ represents the rate of change of $y$ w.r.t $x$ at $x=x_0$
Area of the circle =$\pi r^2\;cm^2$
Radius of the circle =3cm.
$A=\pi r^2$
Differentiating w.r.t $r$ we get,
$\large\frac{dA}{dr}$$=2\pi r$
Substituting for $r$ we get,
$\qquad=2\times \pi\times 3$
$\qquad=6 \pi\;cm^2/cm$
answered Jul 5, 2013 by sreemathi.v
edited Jul 5, 2013 by sreemathi.v
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...