Here is the question: A metal cube of volume 1000cm^3 is melted down and cast into a cuboid 50cm long and 10cm broad. What is the percentage increase in the surface areas of the solids?

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{{{V = 1000}}} cm2
{{{V = s^3}}} where {{{s}}} is the length of all the sides
{{{V = 10*10*10}}} cm2
{{{s = 10}}}cm
The surface area is
{{{A[1] = 6*10*10}}}cm2
{{{A[1] = 600}}}cm2
----------------------
{{{50*10*s = 1000}}} Even though the dimensions change, V can't change
{{{s = 1000/500}}}
{{{s = 2}}}
{{{50*10*2 = 1000}}}
Two of the faces are {{{50*10}}}cm2
Two of the faces are {{{50*2}}}cm2
Two of the faces are {{{2*10}}} cm2
{{{A[2] = 2*50*10 + 2*50*2 + 2*2*10}}}
{{{A[2] = 1000 + 200 + 40}}}
{{{A[2] = 1240}}}
The increase in area is {{{A[2] - A[1] = 1240 - 1000}}}cm2
{{{1240 - 1000 = 240}}}cm2
The percentage increase is {{{240/1000}}} = 24% answer

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