Anonymous asked in Science & MathematicsMathematics · 2 months ago

Need help with this math question?

The radius of a circle increases at a rate of 0.5cms^-1. Find the rate of change in the area of the circle when the area is 25π cm^2

Answer given is 5π cm^2s^-1

I think to know the step to get the answer

1 Answer

  • 2 months ago
    Favourite answer

    A = πr²

    dA/dr = 2πr

    dr/dt = 0.5 cm/s

    dA/dt = dA/dr x dr/dt = (0.5)(2πr) = πr

    when A = 25π, r = √(A/π) = √(25π/π) = 5

    dA/dt = πr = 5π cm²/s

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