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a cube is expanding and its volume is increasing at the rate 96 cubic centimetres/second when the side is 4 cm.Find the rate at which the:

a.side is increasing when the side is 4 cm

b.surface area is increasing when the side is 4cm

V= x^3 A= 6x^2

  • math -

    dV/dt = 3x^2 dx/dt
    96 = 3(4^2)dx/dt
    dx/dt = 96/48 = 2 cm/second

    A = 6x^2
    dA/dt = 12x dx/dt
    dA/dt = 12(4)(2) = 96 cm^2/sec

  • math -

    A spherical balloon is being inflated and its radius is changing at the rate of 2m/minute. When the radius is 4m, find the rate at which the:

    (a).volume is increasing

    V= 3/4 pie r^2

    (b). surface area is increasing

    A = 4 pie r^2

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