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?

Question

20048 views around the world

You can reuse this answer
Creative Commons License

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"#