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The side of a square box is increasing at a rate of 4mm/s and its height is increasing at a rate of 2mm/s. How fast is the volume increasing when the side is 40mm and the height is 100mm.

Can someone just tell me what formula to use?

  • Calculus - ,

    Don't always look for a formula.

    Define your variables and "create" your own formula

    let the square base have sides x by x
    let the height be h

    Volume = x^2 h ----- (from V = length x width x height)
    using the product rule:
    d(Volume)/dt = x^2 dh/dt + h(2x) dx/dt
    we are given all those values

    dV/dt = 40^2 (2) + 100(80)(4)
    = ....

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