Water leaking onto a floor forms a circular pool. the radius of the pool increases at a rate of 8 cm/min. how fast is the area of the pool increasing when the radius is 13 cm?

The area of the pool increasing at the rate of 653.12  when the radius is 13 cm

Step-by-step explanation:

Given:

radius of the pool increases at a rate of 8 cm/min

To Find:

How fast is the area of the pool increasing when the radius is 13 cm ?

Solution:

we are given with the circular pool

hence the area of the circular pool =

A =-----------------------------(1)

The area of the pool os increasing at the rate of 8 cm/min, meaning that the arae of the pool is changing with respect to time t

so differentiating eq (1)  with respect to t , we have

we have to find   with = 8 cm/min and  r =  13cm

substituting the values

answer: 2530

hope this

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step-by-step explanation: