Question

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^2/ft

Answer 1

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`