Question

If the radius of a circle be increasing at a uniform rate of $2cm/s$ . The area of increasing of area of circle, at the instant when the radius is $20cm$ , is

• A. $70\pi c{m}^2/s$
• B. $70c{m}^2/s$
• C. $80\pi c{m}^2/s$
• D. $80c{m}^2/s$

Answer 1

Answer: (C)

Given $\frac{dr}{dt}=2cm/s$, where $r$ be radius of circle and $t$ be the time.
Now, area of circle is giver. by $A=\pi r^2$.
On differentiating w.r.t. $t$, we get
$\frac{dA}{dt}=2\pi r\frac{dr}{dt}$
$\Rightarrow \frac{dA}{dt}=2\pi \cdot 20\cdot 2$
$\Rightarrow \frac{dA}{dt}=80\pi c{m}^2/s$
Thus, the rate of change of area of circle with respect to time is $80\pi c{m}^2/s$.