Did the sphere have a greater surface area or does the cube?

Question

A solid sphere of chocolate has a volume of 288Pi . The chocolate is then melted down and reshaped into a solid cube. Assume no chocolate was wasted.

Did the sphere have a greater surface area or does the cube?

Answer 1

Given that
(4/3)*pi*r^3 = 288*pi
r= 6 units.
Therefore Surface area of the sphere is
4*pi*r^2 = 452.39 cubic units. ------- 1

Also since the chocolate was not wasted when it was molded in to a cube both the volumes of the now formed cube and the sphere should be equal. Therefore

s^3=288*pi
s= 9.67 units.
Therefore it's surface area is
6×s^2 = 6×9.67^2 = 561.28 cu units.---- 2

From 1 and 2 we can say that cube has higher surface area for the same volume as that of the equivalent sphere.