20120301, 23:59  #12 
Oct 2007
Manchester, UK
2×3×227 Posts 

20120302, 01:21  #13  
"Forget I exist"
Jul 2009
Dumbassville
2^{6}×131 Posts 
Quote:
h^3 = 8*R1^3 + 24*R2*R1^2 + 24*R2^2*R1 + 8*R2^3 = 8*(R1^3 + R2^3) + 24*(R2*R1^2 + R2^2*R1) Vh^3 = (8((4/3)*Pi))*(R1^3+R2^3) + 24*(R2*R1^2 + R2^2*R1) that's about how far I got so far with Pari's help. Last fiddled with by science_man_88 on 20120302 at 01:22 

20120304, 16:17  #14 
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2ACC_{16} Posts 
FWIW, it's been snowing here for most of the afternoon. Relatively unusual for this time of year.

20120304, 20:13  #15 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3×29×83 Posts 
Lucky. Everywhere in the US except where I am () has been plastered in snow.

20120304, 20:53  #16 
Jun 2003
The Texas Hill Country
2101_{8} Posts 

20120304, 22:34  #17 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
16065_{8} Posts 
Well okay, everything north and west of Texas. Even AZ and NM got snow at one point.

20120308, 01:03  #18 
Oct 2007
Manchester, UK
2·3·227 Posts 
Is anyone still working on this or should I post the solution?

20120308, 01:37  #19 
"Forget I exist"
Jul 2009
Dumbassville
10000011000000_{2} Posts 

20120308, 20:23  #20 
Oct 2007
Manchester, UK
2×3×227 Posts 
Well I posted a slightly harder version of this problem than the one that was given to me, so I'll post the original now which gives more of a hint to the answer. If there are still no takers after a while I'll post my solution.
Frosty the snowman is made from two uniform spherical snowballs, of radii 2R and 3R. The smaller (which is his head) stands on top the larger. As each snowball melts, its volume decreases at a rate which is directly proportional to its surface area. The constant of proportionality being the same for each snowball. During melting, the snowballs remain spherical and uniform. When frosty is half his initial height, show that the ratio of his volume to his initial volume is 37 : 224. Let V and h denote Frosty's total volume and height, respectively, at time t. Show that, for 2R < h <= 10R: And derive the corresponding expression for 0 <= h < 2R. Sketch dV/dh as a function of h, for 4R >= h >= 0, hence give a rough sketch of V as a function of h. 
20120313, 03:11  #21 
Oct 2007
Manchester, UK
2×3×227 Posts 
I guess noone is going to bite then. I have attached my solution.
Last fiddled with by lavalamp on 20120313 at 03:17 