Question

In: Math

A circular puddle is expanding. How quickly is the radius changing when the area is 50...

A circular puddle is expanding. How quickly is the radius changing when the area is 50 square centimeters and the area is increasing by 4 square centimeters per second?

Expert Solution

we know that area of circular puddle is given by,

differentiate both the side with respect to t we can say that,

---------------------------------------------------------1)

As given we have to find the rate of change of radius when area is 50 square cm and area is increasing by 4 square cm per second

it means we have A = 50, dA/dt = 4

we have,

Hence we can write,

radius can't be negative hence we can write,

we have,

Put them in equation 1) we can write,

rounding to two decimal places we can say that,

Hence we can say that radius is changing at a rate of 0.16 cm per second

milcah answered 2 years ago

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