Odd problem a friend shared with me, which should be simple

[harjutapa]

Hi, I am completely new to this forum. I signed up specifically because this question/problem is irritating my entire circle of friends. None of us can solve it. It is not homework, just an interesting thought experiment one of us came up with. I haven't played with Calculus in a while. Long enough, in fact, that I'm not 100% sure this problem REQUIRES Calc. But I figured this would be the best place to start. I keep getting self-referencing equations that lead me down a rabbit hole. I'm hoping someone here is cleverer than me. So here it is:

A sphere of ice, with an initial volume of 500 cm^3, melts at a rate of 0.25 cm^3 per minute per cm^2 of surface area. Find the equation for the rate of melting at any given time, t.

 

[Deleted member 4993]

Hi, I am completely new to this forum. I signed up specifically because this question/problem is irritating my entire circle of friends. None of us can solve it. It is not homework, just an interesting thought experiment one of us came up with. I haven't played with Calculus in a while. Long enough, in fact, that I'm not 100% sure this problem REQUIRES Calc. But I figured this would be the best place to start. I keep getting self-referencing equations that lead me down a rabbit hole. I'm hoping someone here is cleverer than me. So here it is:

A sphere of ice, with an initial volume of 500 cm^3, melts at a rate of 0.25 cm^3 per minute per cm^2 of surface area. Find the equation for the rate of melting at any given time, t.

What do you mean by "Find the equation for the rate of melting"?

It is given to you!

 

[Ishuda]

Hi, I am completely new to this forum. I signed up specifically because this question/problem is irritating my entire circle of friends. None of us can solve it. It is not homework, just an interesting thought experiment one of us came up with. I haven't played with Calculus in a while. Long enough, in fact, that I'm not 100% sure this problem REQUIRES Calc. But I figured this would be the best place to start. I keep getting self-referencing equations that lead me down a rabbit hole. I'm hoping someone here is cleverer than me. So here it is:

A sphere of ice, with an initial volume of 500 cm^3, melts at a rate of 0.25 cm^3 per minute per cm^2 of surface area. Find the equation for the rate of melting at any given time, t.

To elaborate on what Subhotosh Khan said: The change in volume (dV) must be in units of cm³ which gives
dV = p A cm³
where A is the surface area and has units cm². Thus p has units of cm and, for this problem, is given by
p = $\displaystyle \frac{0.25\, cm^3}{1\, minute\, A}\, dt$
where dt is an incremental time in minutes. Thus
dV = $\displaystyle \frac{0.25\, cm^3}{1\, minute\, A}\, dt\, A\, =\, 0.25\, \frac{cm^3}{minute}\, dt$
or
$\displaystyle \frac{dV}{dt}\, =\, 0.25\, \frac{cm^3}{minute}$