The area A = πr2 of a circular puddle changes with the radius. At what rate does the area change with respect to the radius when r = 5ft? 5π ft^2/ft 5 ft2/ft 10π ft^2/ft 25π ft^…

Question

asked Jan 23, 2020 155k views

1 Answer

Barg · Answer 1 · 2020-01-28T06:24:59+0000

Answer:

Option c)

10π ft^2/ft

Explanation:

Area of the circular puddle = A

=
$\pi r^2$

Where r is the radius of the circular puddle

Since the area of the circular puddle is constantly changing with respect to radius

Therefore, the differential equation hence formed will be

=
(d(A))/(dr)

On putting the value of A

=
$(d(\pi r2))/(dr)$

On differentiating

= 2πr

Hence , Area= A= 2πr

Putting the value of r = 5ft

Area =
$2* 5\pi ft$

=
$10\pi ft^2/ft$