the radius of cylinder increase at the rate of 1cm/s and it's height decrease at the rate of 1cm/s .find the rate of change of its volume when the radius is5cm and the height is 15cm.
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3
Let V be the volume, r be the radius h be the height of the cylinder for the time 't'.
V=πr2hV=πr2h
Given drstdrst=−3;cmsec=−3;cmsec
r=3cmr=3cm
h=5cmh=5cm
dvdt=?dvdt=?
V=πr2hV=πr2h
dVdtdVdt=π[r2dhdt=π[r2dhdt+h2rdrdt]+h2rdrdt]
=π[9×−3+2×2×5×3×2]=π[9×−3+2×2×5×3×2]
=33π=33π
Hence 2 is the correct answer
V=πr2hV=πr2h
Given drstdrst=−3;cmsec=−3;cmsec
r=3cmr=3cm
h=5cmh=5cm
dvdt=?dvdt=?
V=πr2hV=πr2h
dVdtdVdt=π[r2dhdt=π[r2dhdt+h2rdrdt]+h2rdrdt]
=π[9×−3+2×2×5×3×2]=π[9×−3+2×2×5×3×2]
=33π=33π
Hence 2 is the correct answer
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