There are 2 cubes A and B each of volume X cm3. Cube B is cut into smaller cubes each of volume Y cm3. The surface area and volumes of the resulting cubes are compared.
S1: The ratio of volumes of A and B = 1:1
S2 : The ratio of surface areas of A and B = 1:1
S1 is true but S2 is false
The volume is the space occupied by a body .So cutting an object does not change its volume. Therefore cube A and Cube B(after cutting) will have the same volume.
Surface area of a body depends on number of surfaces. So cutting a body creates new surfaces. Hence sum of the TSA of the new cubes would be greater than the TSA of cube A.
Let us try to understand this by converting variables to numbers.
Assume X = 64cm3 and Y = 1cm3.
Therefore number of cubes = 641=64
Volume of cube A = 64 cm3
Volume of cube B after cutting = 64×1=64cm3
Hence the volume is same.
Length of side of cube A = 3√64 = 4cm
Surface area of cube A=6×42 = 96cm2
Length of cube B after cutting = 1cm
Surface area of 1 cube = 6×12 = 6cm2
Surface area of 64 such cubes =64×6=384cm2
Hence surface areas are not same.
Therefore S1 is true and S2 is false