Volume of two cubes each with 64 cm cube,
i.e. Volume first cube = Volume of second cube = 64 cm cube
The two cubes are joined together
Since The general formula for the Volume of cube is a³ where a is the dimension of the cube
So, with the given volume, we can determine the dimension of the cube
[tex]\begin{gathered} \text{Volume = side}^3 \\ \text{Side}^3=Volume \\ a^3=64 \\ a=\sqrt[3]{64} \\ a=4\text{ cm} \end{gathered}[/tex]Thus, the side of the cube is 4cm
Since when two cube combine then the resulting figure will be :
So, the Length of the resulting figure will be equal to the twice of the side of the cube
So,
Length = 4+4 = 8 cm
Breadth= 4cm
Height = 4cm
Since we have to formulate the surface of area of the cubiod
The mathematical expression for the surface area of cubiod is :
[tex]\text{ Surface Area = 2(Length}\times Breadth+Length\times Height+Breadth\times Height)[/tex]Substitute the value and simplify
[tex]\begin{gathered} \text{ Surface Area of cubiod= 2(8}\times4+8\times4+4\times4) \\ S\text{urface Area of cubiod= 2(32}+32+16) \\ S\text{urface Area of cubiod= 2}\times(80) \\ S\text{urface Area of cubiod= }160cm^2 \end{gathered}[/tex]Answer : D) 160 cm²
