water is dripping out from a conical funnel of semi vertical angle 45 at uniform rate of 2 cm^2/s (is its sure areea) through a tiny hole at vertical of the bottom wht is the rate of decrese of slant height when the slant height of water is 4cm

let r be the radius , h be the height and V be the volume of the funnel at any time t.
let l be the slant height of the funnel.
given: semi-vertical angle = 45 deg
in the triangle ADE;
sin45=DEAE12=rlcos45=ADAE12=hlr=l2  and h=l2....(2)
therefore the eq(1) can be rewritten as:
differentiating wrt t :
since it is given that rate of change (decrease) of volume of water wrt t is
dVdt=-2 cm3/sec
dldt=22πl2*(-2)=-42πl2dldtat l = 4=-42π*(4)2=-24πcm/sec

hope this helps you

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