calc

When the height of a cylinder is 12 cm and the radius is 4 cm, the circumference of the cylinder is increasing at a rate of pie/4 cm/m in, and the height of the cylinder is increasing four times faster than the radius. How fast is the volume of the cylinder changing?

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  1. since C = 2πr, dC/dt = 2π dr/dt
    Since dC/dt = π/4, dr/dt = (π/4)/(2π) = 1/8 cm/min

    v = πr^2h
    dv/dt = 2πrh dr/dt + πr^2 dh/dt
    = 2π*4*12*(1/8) + π*16*(1/2)
    = 20π cm^3/min

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