Rates of change! (1 Viewer)

[icecubeX]

I need help. ><" this question is weird.

"Suppose that a raindrop is a perfect square. Assume that throughtout condensation, the raindrop accumulates moisture at a rate proportional to its surface area. Show that the radius increases at a constant rate."

and yes this is all the info they give you.

 

[pwoh]

Do you mean sphere? Have never heard of squares with radii...

If so:
V= (4/3)pi * r^3 ( volume)
A= 4pi r^2 ( surface area)

dV/dt = k * 4pi r^2 (k is a constant)

dV/dt = dV/dr * dr/dt (chain rule)

dr/dt = dV/dt / dV/dr
= [k * 4 pi r^2] / [(4/3)pi * 3r^2]
= [k] / [(1/3) * 3] = k

 

[Tofuu]

Do you mean sphere? Have never heard of squares with radii...

true true

 

[icecubeX]

See the problem is i dunno what the thing would look like!
is it a cube shape or a flat prism? dunno

It'd be extremely helpful if i knew what it looked like. =/

 

[pwoh]

See my reply above, it works perfectly if it were a sphere. If it wasn't for gravity and the like, raindrops would be spheres. Plus it can't be a square, squares have no volume...question was a typo probably? xD

 

[icecubeX]

LOL i dunno but yes your way makes sense. At first i tried to think of it as a cube.
Failed... still had like x in the answer ><"

but yeah thanks! =)