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calculus

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a spherical snowball with diameter 4 inches is removed from the freezer in June and begins melthing uniformly such that it is shrinking 2 cubic inches per minute. How fast ( in square inches per minute) is the surface area decreasing when the radius is 1 inch?

  • calculus -

    ..it is shrinking 2 cubic inches per minute ----> dV/dt = -2 cubic inches/min

    V = (4/3)pi(r^3)
    dV/dt = 4pi(r^2)dr/dt
    when r - 1 and dV/dt = -2

    -2 = 4pi(1)dr/dt
    dr/dt = -1/(2pi)

    but A = 4pi(r^2)

    then dA/dt = 8pi(r)dr/dt
    so again when r=1
    dA/dt = 8pi(1)(-1/2pi)
    =-4 square inches/min

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