Question

the radius of a circle is increasing at the rate of 0.1 cm per second when radius of circle is 5 cm then the rate of change of are is

Answer 1

Given dr/dt = 0.1 cm/sec , r= 5 cm

Area of circle = πr²

DA/dt = d(πr²)/dt

       = 2πrdr

Putting value of dr and r

dA/ dt = 2*3.14*5*0.1 cm²/ sec

          = 3.14 cm²/ sec

Answer 2

Answer:

3.14 cm square per seconds  ( approx )

Step-by-step explanation:

Since, we know that,

Area of a circle is,

$A=\pi r^2$

Differentiating with respect to t, ( time in seconds ),

$\frac{dA}{dt}=\pi (2 r) \frac{dr}{dt}$

We have,

r = 5 cm, $\frac{dr}{dt}=0.1\text{ cm per seconds}$

$\implies \frac{dA}{dt} = \pi ( 2\times 5) \times 0.1 = \pi=3.14\text{ cm square per seconds }$