Question

If a circular iron sheet of radius $30cm$ is heated such that its area increases at the uniform rate of $6\pi c{m}^2/hr$, then the rate (in mm / hr) at which the radius of the circular sheet increases is.

• A. $2.0$
• B. $1.0$
• C. $1.1$
• D. $0.1$

Answer 1

The correct option is B $1.0$

Given, $r=30cm,\frac{dA}{dt}=6\pi c{m}^2/hr$

we know, $A=\pi r^2$
$\frac{dA}{dt}=2\pi r\frac{dr}{dt}$
$6\pi =60\pi \frac{dr}{dt}$
$\therefore \frac{dr}{dt}=\frac{1}{10}$
$\therefore 10\frac{dr}{dt}\left(mm/hr\right)=\frac{10}{10}=1.0$