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

Answer:

$\frac{dl}{dt} = -1.75\,\frac{cm}{min}$

Step-by-step 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:

$\frac{dV}{dt} = 3\cdot l^{2}\cdot \frac{dl}{dt}$

$\frac{dl}{dt}= \frac{1}{3\cdot l^{2}}\cdot \frac{dV}{dt}$

The rate of change is:

$\frac{dl}{dt} = \frac{1}{3\cdot (8\,cm)^{2}}\cdot \left(-42\,\frac{cm^{3}}{min}\right)$

$\frac{dl}{dt} = -1.75\,\frac{cm}{min}$