Question 1114772
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The volume of the cube is given by the equation
{{{V = s^3}}}<br>
The relationship between the rate of change of volume and the rate of change of edge length is found by differentiating that equation:
{{{dV/dt = 3s^2*(ds/dt)}}}<br>
It is given that the volume is increasing at a rate of 0.63 cm^3/sec when the edge length is 4 cm, so<br>
{{{0.63 = 3(4^2)*(ds/dt)}}}
{{{ds/dt = 0.63/48 = 0.013125}}}<br>
Answer: At the moment when the edge length is 4 cm, it is increasing at the rate of 0.013125 cm/sec.