Question

The rate of change of the area of a circle with respect to its radius r, when r = 3 cm, is ______.

Answer 1

The rate of change of the area of a circle with respect to its radius r, when r = 3 cm, is 6π cm.

Explanation:

Area of circle with radius r = πr²

A = πr²

Differentiate w.r.t. r

`"dA"/"dr" = π(2r)`

`"dA"/"dr" = 2πr`

When, r = 3 cm

`"dA"/"dr"}_(r = 3) = 2π(3)`

= 6π cm square