Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of

Question

Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 2 m/s, exactly how fast (in m2/s) is the area of the spill increasing when the radius is 39 m?

in progress 0
Neala 5 years 2021-07-14T14:13:38+00:00 1 Answers 214 views 0

Answers ( )

  1. Verity
    1
    2021-07-14T14:15:30+00:00
    Reply

    Explanation:

    The area of a circle of radius r is given by

    A = \pi r^2

    Taking the derivative of A with respect to time t, we get

    \dfrac{dA}{dt} = 2\pi r \dfrac{dr}{dt}

    We also know that

    \dfrac{dr}{dt} = 2\:\text{m/s}\:\text{at}\:r = 39\:\text{m}

    \dfrac{dA}{dt} = 2\pi (39\:\text{m})(2\:\text{m/s})= 490\:\text{m}^2\text{/s}

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )