Acircular cloud of poison gas from a factory explosion is expanding so that t hours after the explosion the radius of the cloud is r(t)=50+20t meters. how fast is the area of the cloud increasing 4 hours after the explosion?

The area of cloud increasing 4 hours after the explosion is 16328 square meters.

Explanation:

The radius of the cloud is R(t) = 50 + 20t

We need to find how fast the area of cloud increasing when t = 4 hours.

Area of a circle A =

Now we have to find the derivative with respect to "t"

 ----------(1)

We know that r = 50 +  20t, let's find the derivative with respect to "t"

Now plugin

Now let's find . Plug in t =4, we get

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We know that the value of

So,

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Therefore, the area of cloud increasing 4 hours after the explosion is 16328 square meters.

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