Question

If a cube with a surface area of 216 square inches has its dimensions divided in half, what will be the volume of the new cube?

Answer 1

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.

Step-by-step explanation:

The surface area of the cube is given by the formula:

`A=6*(side)^2`
`\begin{gathered} 216=6(side)^2 \\ 36=(side)^2 \end{gathered}`

Take the root on both sides.

`side\text{ = 6 in.}`

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 =

`=(6)/(2)\text{ = 3 in.}`

So the volume of the new cube

`\begin{gathered} =(side)^3 \\ =(3)^3 \\ =27\text{ cubic in.} \end{gathered}`

Final Answer:

`27\text{ cubic in.}`