Given:
The surface area of the cube A = 216 square inches
Required:
To find the volume of the new cube when the dimensions are divided in the half.
Explanation:
The surface area of the cube is given by the formula:
[tex]A=6\times(side)^2[/tex][tex]\begin{gathered} 216=6(side)^2 \\ 36=(side)^2 \end{gathered}[/tex]Take the root on both sides.
[tex]side\text{ = 6 in.}[/tex]Thus the side of the cube is 6 in.
Now the new cube has the dimensions half of the given cube.
So the side of the new cube =
[tex]=\frac{6}{2}\text{ = 3 in.}[/tex]So the volume of the new cube
[tex]\begin{gathered} =(side)^3 \\ =(3)^3 \\ =27\text{ cubic in.} \end{gathered}[/tex]Final Answer:
[tex]27\text{ cubic in.}[/tex]