Question

) An cube of ice was melting in the Arizona sun. The Volume of the cube was decreasing at a rate of 42 cubic centimeters per minute at the moment that one side of the cube was 8 centimeters long. How fast was the length of the side of the cube changing

Answer 1

`(dl)/(dt) = -1.75\,(cm)/(min)`

Explanation:

The volume formula for the cube is:

`V = l^(3)`

The rate of the change of the cube side is obtained by deriving the expression in terms of time:

`(dV)/(dt) = 3\cdot l^(2)\cdot (dl)/(dt)`

`(dl)/(dt)= (1)/(3\cdot l^(2))\cdot (dV)/(dt)`

The rate of change is:

`(dl)/(dt) = (1)/(3\cdot (8\,cm)^(2))\cdot \left(-42\,(cm^(3))/(min)\right)`

`(dl)/(dt) = -1.75\,(cm)/(min)`