A cube of ice is melting and the volume is decreasing at a rate of 3 cubic m/s. How fast is the height decreasing when the cube is 6 inches in height?

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Answer 1 · 2015-04-02T22:22:18

The height is decreasing at a rate of $0.028"in/s"$

$V=h^3$

$(dV)/(dh)=3h^2$

When $h=6$ , $(dV)/(dh)=3xx6^2=108"in"^2$

$(dV)/(dt)=-3"in"^3"/s"$

$(dV)/(dt)=(dV)/(dh)xx(dh)/(dt)$

$-3=108xx(dh)/(dt)$

$(dh)/(dt)=(-3)/(108)=-0.028"in/s"$