The Changing Cube

Calculus Level pending

The surface area of a cube is changing at a rate of 3.6 unit 2 /second 3.6 \text{ unit}^2\text{/second} . At what rate is its volume changing (in cu units per second) when its side is equal to 10 units?


The answer is 9.

Arkajyoti Banerjee by Arkajyoti Banerjee , 20, India

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1 solution

Let the surface area= S S , cubic side= x x , and volume= V V . Then according to the question,

Now, we need to find the rate of change of its volume with respect to time. That is,

Therefore, when x = 10 x=10 , its volume will be changing at the rate of 0.9 ( 10 ) 0.9(10) , i.e., 9 9 cu units per second.

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