Question 122283
The total surface area of a cube with edge 'a' is given by
{{{S = 6a^2}}}.
If edge is doubled, then the edge '2a' in the above formula and so the new total surface area is
{{{S[new] = 6(2a)^2 = 4x(6a^2) = 4S}}} i.e. 4 times original total surface area.
If edge is trebled, then the edge '3a' in the above formula and so the new total surface area is
{{{S[new] = 6(3a)^2 = 9x(6a^2) = 9S}}} i.e. 9 times original total surface area.
If edge is halved, then the edge {{{a/2}}} in the above formula and so the new total surface area is
{{{S[new] = 6(a/2)^2 = (6a^2)/4 = S/4}}} i.e. one-fourth original total surface area.