*Cool* ice cream problem
Given that when the volume of an ice cream at an instant is x and, at that instant, it melts at a rate of 3 x ^2 per second, how long would it take, in seconds, for an ice cream of volume 10 to melt completely? (Round your answer to the nearest second)
The answer is 2.
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1 solution
Since the gradient of the graph of the volume of the ice cream is -3x^2, by integration, we find that the graph of the volume of the ice cream is given by -x^3+c. Since, when x=0, -x^3+c=10, c=10. Therefore, solving for -x^3+10=0, we find that x is the cube root of 10 which is approximately equal to 2. Fortunately ice cream in real life don't melt so fast~~~