The area of a circular oil slick on the surface of the sea is increasing at a rate of [150m^2/s] how fast is the radius changing when: a) the radius is 25 m b) the area is [1000…

Question

asked Jan 11, 2021 145k views

1 Answer

Mike James · Answer 1 · 2021-01-17T19:49:47+0000

Answer with Step-by-step explanation:

We are given that

(dA)/(dt)=150m^2/s

a.Radius =25 m

We have to find rate of change of radius.

We know that

Area of circle,
$A=\pi r^2$

Differentiate w.r.t time

$(dA)/(dt)=2\pi r(dr)/(dt)$

Substitute the values then we get

$150=2\pi (25)(dr)/(dt)$

$(dr)/(dt)=(150)/(50\pi)=(3)/(\pi) m/s$

$(dr)/(dt)=(3)/(\pi) m/s$

b.A=
1000m^2

Substitute the values then we get

$1000=\pi r^2$

$\pi=3.14$

r^2=(1000)/(3.14)

$r=\sqrt{(1000)/(3.14)}=17.8m$

$(dA)/(dr)=2\pi r(dr)/(dt)$

Substitute the values then we get

$150=2\pi(17.8)(dr)/(dt)$

$(dr)/(dt)=(150)/(2\pi(17.8))=(150)/(35.6\pi)$ m/s

$(dr)/(dt)=(75)/(17.8\pi)$ m/s