Question

Radius of a circle, r is increasing at a constant rate dr/dt=k. At the moment when radius is r, the rate of change of area is​

Answer 1

area of circle , A = πr²

here it is clear that Area is function of radius. now differentiating area with respect to time.

i.e., dA/dt = d(πr²)/dt

or, dA/dt = π × d(r²)/dt

or, dA/dt = π × 2r × dr/dt

or, dA/dt = 2πr × dr/dt

it is given that radius is increasing at a constant rate , dr/dt = k.

so, area of circle is increasing at the rate , dA/dt = 2πr × k

at the moment radius is r

then, change in area , dA/dt = 2πrK

so, required answer is dA/dt = 2πrK

Answer 2

Answer:

Here is your answer

Explanation:

area of circle , A = πr²

here it is clear that Area is function of radius. now differentiating area with respect to time.

i.e., dA/dt = d(πr²)/dt

or, dA/dt = π × d(r²)/dt

or, dA/dt = π × 2r × dr/dt

or, dA/dt = 2πr × dr/dt

it is given that radius is increasing at a constant rate , dr/dt = k.

so, area of circle is increasing at the rate , dA/dt = 2πr × k

at the moment radius is r

then, change in area , dA/dt = 2πrK

so, required answer is dA/dt = 2πrK