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?

Answer 1

Ezra Adams

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"#

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Answer 2

Aurora Alvarado

To find the rate at which the height is decreasing when the cube is 6 inches in height, you can use related rates. Since the cube is melting, its volume is decreasing at a rate of 3 cubic meters per second. Let $V$ represent the volume of the cube and $h$ represent its height. The volume of a cube is given by $V = h^3$ . Differentiating both sides with respect to time $t$ , we get $\frac{dV}{dt} = 3h^2 \frac{dh}{dt}$ . Given that $\frac{dV}{dt} = -3$ (negative because the volume is decreasing) and when $h = 6$ , you can solve for $\frac{dh}{dt}$ . Plugging in the values, you'll get $\frac{dh}{dt} = -\frac{1}{4}$ meters per second.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.