Question

please solve the question immediately ​

Answer 1

Option - (4)

Given,

==> dr/dt = 0.1 m/s

To Find:

==> dA/dt

We know,

==> Area of a plate ( in the shape of circle ) = πr²

==> A = πr²

Differentiate both sides w.r.t t

==> dA/dt = d(πr²)/dt

==> dA/dt = π { d(r²)/dt }

==> dA/dt = π { 2r × dr/dt }

==> dA / dt = π × 2r × 0.1

==> dA/dt = 0.2πr

At r = 5/11 cm

==> dA/dt = 0.2 × 5/11 × 22/7

==> dA/dt = 0.2 × 5 × 2 / 7

==> dA/dt = 2/7

==> dA/dt = 0.285714 cm²/s

or

==> dA/dt = 0.29 cm²/s

Hence, the rate at which area will increase when the radius is 5/11 cm is 0.29 cm²/s

Answer 2

option 4 is the correct answer .

hope it help you ✌