SOLUTION: A metal cube expands due to it being heated. When the length of an edge of the cube is 4 cm, the volume of a metal cube is increasing at the rate of 0.63 cm3 s-1. What is the

Algebra ->  Test -> SOLUTION: A metal cube expands due to it being heated. When the length of an edge of the cube is 4 cm, the volume of a metal cube is increasing at the rate of 0.63 cm3 s-1. What is the      Log On


   

Question 1114772: A metal cube expands due to it being heated. When the length of an edge of the cube is 4 cm, the volume of a metal cube is increasing at the rate of 0.63 cm3 s-1. What is the rate of change of an edge at this time?
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The volume of the cube is given by the equation
V+=+s%5E3

The relationship between the rate of change of volume and the rate of change of edge length is found by differentiating that equation:
dV%2Fdt+=+3s%5E2%2A%28ds%2Fdt%29

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

0.63+=+3%284%5E2%29%2A%28ds%2Fdt%29
ds%2Fdt+=+0.63%2F48+=+0.013125

Answer: At the moment when the edge length is 4 cm, it is increasing at the rate of 0.013125 cm/sec.