If the rate of increase of the radius of a circle is 5 cm/s, then the rate of increase of its area, when the radius is 20 cm, will be

Question

If the rate of increase of the radius of a circle is 5 cm/s, then the rate of increase of its area, when the radius is 20 cm, will be (A) 10 π (B) 20 π (C) 200 π (D) 400 π

Tardigrade Admin · Accepted Answer

Since, area of circle, A=π r2 On differentiating w.r.t. t, we get (dA/dt)=2π r (dr/dt) =2π⋅20⋅5=200π

Q. If the rate of increase of the radius of a circle is $5 c m / s$ , then the rate of increase of its area, when the radius is $20 c m$ , will be

$10 π$

$20 π$

$200 π$

$400 π$

Since, area of circle, $A = π r^{2}$

On differentiating w.r.t. t, we get

$\frac{d A}{d t} = 2 π r \frac{d r}{d t}$

$= 2 π \cdot 20 \cdot 5 = 200 π$

Q. If the rate of increase of the radius of a circle is 5cm/s, then the rate of increase of its area, when the radius is 20cm, will be

10π

20π

200π

400π