Question

Find the rate of change of area of a circle with respect to its radius r when r=3cm.​

Answer 1

AnsWer :

6π cm² / s.

GiveN :

• r = 3 cm.

To FinD :

Find the rate of change of area of a circle with respect to its radius r

SolutioN :

✎ We know,

$\tt \dagger \: \: \: \: \: Area \: of \: Circle = \pi {r}^{2} .$

☯ Let's differentiate w.r.t

$\tt \longmapsto \dfrac{dA}{dt} = \pi2r.$

$\tt \longmapsto \dfrac{dA}{dt} = 2 \pi r.$

$\rule{100}2$

✎ Now,

• When, r = 3 cm.

$\tt \longmapsto \dfrac{dA}{dt} =2 \pi r.$

$\tt \longmapsto \dfrac{dA}{dt} =2 \pi 3.$

$\tt \longmapsto \dfrac{dA}{dt} =6 \pi c {m}^{2}/ s.$

✡ Therefore, the value of rate of change of area of a circle is 6π cm² /s.