A parked car dripping transmission fluid is creating a circular puddle whose area (in square inches) is Aequalspir2 where r is the radius of the circle in inches. Find the rate at which the area of the puddle is increasing at the instant when the radius is 9 inches and increasing at a rate of 3 inches per minute.

Question

Remington Marshall

Mathematics

9 January, 13:53

A parked car dripping transmission fluid is creating a circular puddle whose area (in square inches) is Aequalspir2 where r is the radius of the circle in inches. Find the rate at which the area of the puddle is increasing at the instant when the radius is 9 inches and increasing at a rate of 3 inches per minute.

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Answers (1)

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Kyler Dorsey · Answer 1

dA/dt = 169,56 in²/min

Step-by-step explanation:

We have a circular puddle and its area is:

A = π*r² (1) r is the radius of the circular puddle

Differentiating on both sides of the equation we get:

dA/dt = π*2*r*dr/dt (1)

In that expression we know

r = 9 inches and dr/dt = 3 in/min. Therefore plugging these values in equation (1)

dA/dt = π*2*9*3

dA/dt = 169,56 in²/min